[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[10, 0, -4, 1, -5],
 [0, -7, -10, 11, 4],
 [-4, -10, 12, -2, 10],
 [1, 11, -2, -11, 2],
 [-5, 4, 10, 2, 6]]

Present the answer in LaTex format: \boxed{Your answer}

dataset: MATH


[User]
Determine the value of det(A) where A =
[[-6, 6, 10, 1, 12],
 [6, -2, -10, -7, -6],
 [10, -10, -9, -5, 1],
 [1, -7, -5, 7, 0],
 [12, -6, 1, 0, -12]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[-8, 8, 10, 7, 10],
 [-11, -4, 9, -1, 7],
 [0, 6, 5, -5, 13],
 [0, -6, -6, -13, -5],
 [-2, -12, 0, -13, 8]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[-3, -5, -6, -4, 14],
 [-5, -10, -3, 2, -4],
 [-15, 4, 11, 7, 15],
 [-5, 7, 13, 2, -8],
 [4, 1, -4, 2, 12]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[14, -6, -11, 9, 1],
 [-7, 14, 5, 3, -5],
 [-13, -12, -1, -9, -9],
 [10, 1, -3, 3, -2],
 [0, -6, 6, -13, -9]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[-1, 0, 2, 2, 4],
 [0, -5, 0, -2, -4],
 [2, 0, -11, 2, -10],
 [2, -2, 2, -13, 0],
 [4, -4, -10, 0, -9]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[11, 5, -4, -10, -2],
 [-5, 15, 8, 3, 12],
 [-12, 12, -3, 9, -12],
 [13, 14, -9, -15, 0],
 [-1, -9, 1, 6, -7]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[9, -12, -2, -11, 12],
 [0, 15, 14, -15, -13],
 [0, 0, -14, 11, 12],
 [0, 0, 0, 11, -3],
 [0, 0, 0, 0, -7]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[12, 6, -4, 11, -9],
 [0, -3, -7, -13, 5],
 [3, 2, -12, -9, 15],
 [-8, -6, 7, 0, 10],
 [10, -2, 4, 2, -15]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[14, -12, 6, 8, 14],
 [15, 0, -6, 5, 14],
 [14, -4, -13, 6, 15],
 [-13, 0, -4, -2, -5],
 [-5, 6, -5, 2, 5]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[11, 2, -10, -3, 14],
 [2, 13, 0, -2, -1],
 [-10, 0, 15, 4, 2],
 [-3, -2, 4, 3, 9],
 [14, -1, 2, 9, 8]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[-10, -4, -10, 13, 7],
 [7, -15, -10, -5, 8],
 [-13, 5, 10, 5, -1],
 [-13, -11, 4, -2, 13],
 [7, 3, 11, 7, -15]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[-9, 15, 9, -14, 13],
 [0, 5, -6, -8, 13],
 [0, 0, -15, 6, -2],
 [0, 0, 0, 5, 4],
 [0, 0, 0, 0, -3]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[5, -15, 12, -6, -4],
 [-3, 3, 0, -3, -8],
 [-2, 14, 4, 6, 0],
 [-11, 12, -4, 3, -4],
 [-10, -4, 6, 4, 8]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[-7, -1, 6, -5, 1],
 [-1, -8, 4, 2, 8],
 [6, 4, 0, 5, -10],
 [-5, 2, 5, 3, 5],
 [1, 8, -10, 5, -9]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[-14, -11, -7, 4, 8],
 [0, 12, -3, -15, -5],
 [0, 0, 10, 5, 6],
 [0, 0, 0, -11, 1],
 [0, 0, 0, 0, 4]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[4, -2, 0, 2, 2],
 [-2, -5, -2, -6, 2],
 [0, -2, -6, 7, -3],
 [2, -6, 7, -15, 7],
 [2, 2, -3, 7, -5]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[-7, -7, 12, 4, 12],
 [5, 4, 4, 11, 13],
 [14, -12, 3, 0, 2],
 [-6, 5, 13, 15, 10],
 [8, -1, -8, -4, 2]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[0, 0, -8, -2, -11],
 [-6, 0, 3, 7, -8],
 [-9, 7, 4, 10, -13],
 [-10, 12, -8, -11, -10],
 [13, -7, 9, 15, -1]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[12, 7, -10, -1, -1],
 [0, 9, -12, 0, 9],
 [0, 0, 7, -14, -13],
 [0, 0, 0, -12, 8],
 [0, 0, 0, 0, 15]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[9, -15, 12, 6, 8],
 [0, -11, -13, 4, 13],
 [0, 0, -1, -6, -7],
 [0, 0, 0, 6, -4],
 [0, 0, 0, 0, -15]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[14, -3, 10, -10, 6],
 [0, -14, -12, 14, 12],
 [0, 0, -4, 14, 11],
 [0, 0, 0, -14, 10],
 [0, 0, 0, 0, 15]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[6, 3, 2, 6, 7],
 [2, -11, 13, 14, -14],
 [6, 4, 3, 2, 2],
 [10, -10, 0, -2, 8],
 [-8, -10, -1, 0, -14]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[4, -2, -1, -3, 13],
 [-10, -13, 5, -7, 4],
 [6, 9, -4, -13, -10],
 [-9, -14, 6, 8, -2],
 [-9, -3, 4, 11, 12]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[-10, -8, 10, 2, -10],
 [-8, -11, 3, -10, 9],
 [10, 3, -2, 9, 0],
 [2, -10, 9, 7, 4],
 [-10, 9, 0, 4, 0]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[5, 2, 12, 1, -6],
 [6, 13, -13, 0, 7],
 [3, -15, -10, 2, -8],
 [7, -8, 15, 6, -4],
 [12, -11, 6, 2, 0]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[0, -8, 6, -3, 0],
 [-8, 9, 6, 0, -6],
 [6, 6, -7, -8, 2],
 [-3, 0, -8, -1, 2],
 [0, -6, 2, 2, -9]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[-2, 8, -1, 14, 6],
 [0, 6, -12, -11, 8],
 [0, 0, -6, 13, 11],
 [0, 0, 0, 1, -2],
 [0, 0, 0, 0, -2]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[-12, 4, 6, 14, 8],
 [4, -4, 0, -8, -3],
 [6, 0, 12, -11, -2],
 [14, -8, -11, -1, -1],
 [8, -3, -2, -1, 3]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[6, 11, 6, -10, 11],
 [0, -1, 6, 0, 13],
 [0, 0, 7, -15, -9],
 [0, 0, 0, 4, 13],
 [0, 0, 0, 0, 1]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[11, -2, 0, -4, -12],
 [-2, 0, 0, -9, 4],
 [0, 0, 15, 0, 2],
 [-4, -9, 0, 3, -1],
 [-12, 4, 2, -1, -2]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[-13, 1, -15, -6, -1],
 [0, 10, -1, -10, -15],
 [0, 0, 15, -9, -13],
 [0, 0, 0, 6, -11],
 [0, 0, 0, 0, 6]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[7, 13, -8, 3, -4],
 [-6, 10, -8, 12, 3],
 [-7, -11, 2, 14, -6],
 [-2, -14, -2, 11, 7],
 [7, -8, -13, 14, -11]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[-15, -13, -8, -10, 13],
 [0, -4, 11, 12, -1],
 [0, 0, 1, -5, 6],
 [0, 0, 0, 14, 2],
 [0, 0, 0, 0, -15]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[-10, 4, 9, 5, 7],
 [7, -4, 10, 15, 4],
 [-5, -12, -12, 13, -8],
 [-12, 0, -13, 5, 1],
 [6, -4, 2, 7, 9]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[10, -12, -15, 13, 8],
 [0, 15, 10, 0, -12],
 [0, 0, -6, -7, 6],
 [0, 0, 0, -11, -6],
 [0, 0, 0, 0, 8]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[-12, -2, 1, -15, -13],
 [14, -4, -11, -4, 10],
 [4, 0, -15, -8, -15],
 [-5, -1, 10, -6, -3],
 [-4, 9, -11, 8, 4]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[-12, 7, -13, -6, -13],
 [-15, -9, -6, 8, 2],
 [11, -2, 7, -6, 11],
 [-4, -5, 2, -7, 11],
 [12, -2, 3, 10, -2]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[2, 6, 0, 0, -2],
 [6, -3, 4, -1, -2],
 [0, 4, -15, 0, -2],
 [0, -1, 0, 10, -4],
 [-2, -2, -2, -4, -3]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[4, -7, 12, -2, 0],
 [6, 9, 15, -7, -8],
 [-9, 4, -10, -12, -14],
 [-8, 1, -13, 0, 11],
 [12, -14, 14, 6, 10]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[-12, 2, -15, -14, 3, -6],
 [-1, 5, 1, -9, 8, 0],
 [-2, -2, 7, 6, -11, -4],
 [4, 10, 3, 2, 10, 8],
 [10, -2, 11, -11, -1, -10],
 [9, -12, 3, -13, 14, -1]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[7, -2, 8, 4, -8, 6],
 [-2, 11, 6, 2, 5, 9],
 [8, 6, 15, 1, 0, 7],
 [4, 2, 1, -9, 6, -2],
 [-8, 5, 0, 6, 13, -10],
 [6, 9, 7, -2, -10, 15]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[14, -15, 7, -4, 10, 13],
 [0, -3, 5, -12, -1, 9],
 [0, 0, -1, -9, 14, -14],
 [0, 0, 0, -6, 13, 1],
 [0, 0, 0, 0, 11, -8],
 [0, 0, 0, 0, 0, -14]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[2, 3, -2, 4, -15, -14],
 [0, 6, -15, -11, 7, -5],
 [1, -12, 4, 13, -1, -3],
 [-8, 4, -4, -9, -13, -14],
 [8, -6, -1, 12, 5, 9],
 [14, 5, -1, 15, -5, -4]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[8, -11, -2, -6, -7, 5],
 [13, 7, 3, 1, 9, -14],
 [-5, -11, 5, -7, -15, 1],
 [6, -8, -11, -15, -10, -7],
 [14, -2, 12, -5, -8, 11],
 [1, 5, -14, 13, 9, 13]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[3, -5, 2, -6, 0, 4],
 [-5, -1, -2, -8, 2, -5],
 [2, -2, 14, 10, -4, -2],
 [-6, -8, 10, -4, 4, -7],
 [0, 2, -4, 4, 12, 8],
 [4, -5, -2, -7, 8, 11]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[-6, 6, 1, 3, -12, 8],
 [0, -3, -10, -1, 12, -6],
 [0, 0, -6, 14, -11, 13],
 [0, 0, 0, -3, -10, 3],
 [0, 0, 0, 0, -1, 15],
 [0, 0, 0, 0, 0, -4]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[1, 0, -2, -2, 2, 10],
 [0, -6, 4, 0, 3, 2],
 [-2, 4, 2, 0, -6, -2],
 [-2, 0, 0, -4, -5, 10],
 [2, 3, -6, -5, -4, 5],
 [10, 2, -2, 10, 5, 1]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[2, 13, 2, -6, -5, 3],
 [0, -15, -4, 12, 6, 4],
 [0, 0, 7, 15, 7, -15],
 [0, 0, 0, -6, 13, -4],
 [0, 0, 0, 0, 12, 11],
 [0, 0, 0, 0, 0, -6]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[-10, 8, -2, -6, 12, -1],
 [0, -5, -5, 14, 5, 11],
 [0, 0, 9, -4, -7, -5],
 [0, 0, 0, -1, -1, 1],
 [0, 0, 0, 0, -4, -6],
 [0, 0, 0, 0, 0, -7]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[13, 10, -6, -9, 9, 1],
 [0, -10, -1, -7, -14, 1],
 [0, 0, -2, -4, -12, 4],
 [0, 0, 0, -11, 3, 7],
 [0, 0, 0, 0, 6, -13],
 [0, 0, 0, 0, 0, -12]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[-11, 7, 15, 14, -8, -1],
 [0, 2, 5, 7, -3, 1],
 [0, 0, 5, 5, -14, 15],
 [0, 0, 0, 13, 12, -7],
 [0, 0, 0, 0, -4, -14],
 [0, 0, 0, 0, 0, 12]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[13, 10, 0, -1, -4, 0],
 [10, 7, 8, -8, 2, -2],
 [0, 8, -15, -7, -8, -2],
 [-1, -8, -7, -1, 0, 4],
 [-4, 2, -8, 0, 8, -2],
 [0, -2, -2, 4, -2, 1]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[-4, 15, 1, 12, -4, 4],
 [0, 7, 14, -13, 9, 14],
 [0, 0, -13, -8, -6, -14],
 [0, 0, 0, 4, 14, 9],
 [0, 0, 0, 0, -11, 2],
 [0, 0, 0, 0, 0, -8]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[12, 5, 14, -14, -13, -15],
 [-6, 3, -10, 7, 11, -10],
 [-7, 14, 7, 8, 10, 1],
 [12, -15, 8, 4, 0, 12],
 [11, -9, 2, 0, -1, 5],
 [9, -6, 3, 13, 11, 12]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[-3, -6, -2, -4, 2, 4],
 [-6, -4, -2, 2, 6, 0],
 [-2, -2, 8, 3, -7, 6],
 [-4, 2, 3, 0, 1, 3],
 [2, 6, -7, 1, 5, -6],
 [4, 0, 6, 3, -6, 8]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[15, 9, 15, -15, -9, -5],
 [8, 2, 11, 2, -15, -4],
 [11, 2, 7, -12, -4, 10],
 [4, -1, 11, 6, 12, 1],
 [-6, 1, -3, 3, 14, -13],
 [-2, 4, -2, -2, 1, -13]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[6, 15, -15, 9, -1, -10],
 [-11, 11, -2, -12, 8, 2],
 [-15, 2, 9, 3, -7, 4],
 [14, -5, 10, 8, -11, -3],
 [10, 10, 2, 4, 10, 13],
 [15, 13, 2, -13, 13, -12]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[-11, 1, -15, -8, -8, -13],
 [0, -2, 1, 9, 11, 3],
 [0, 0, 10, 9, 14, 7],
 [0, 0, 0, 15, -2, 5],
 [0, 0, 0, 0, -14, 7],
 [0, 0, 0, 0, 0, -6]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[11, 11, 6, 6, 5, 11],
 [0, -2, 8, 4, -4, -9],
 [0, 0, -14, 0, -14, -10],
 [0, 0, 0, 3, 7, -3],
 [0, 0, 0, 0, -8, -10],
 [0, 0, 0, 0, 0, -13]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[-2, 7, -1, -4, 13, 13],
 [0, 11, 3, -5, -11, -7],
 [0, 0, -2, -12, 7, -6],
 [0, 0, 0, 15, 10, -3],
 [0, 0, 0, 0, 2, -8],
 [0, 0, 0, 0, 0, -2]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[0, -8, 1, -3, 10, -6],
 [-2, -1, -2, -7, 8, -1],
 [7, 6, 13, 11, 12, -4],
 [8, -3, 9, 7, 6, 4],
 [4, 7, -8, -3, -7, 6],
 [-5, 3, -5, -8, 4, 2]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[13, 12, -7, -7, 0, 15],
 [1, -8, 1, -15, 11, 5],
 [5, -9, 5, -6, -5, 14],
 [-14, -8, -10, -2, 15, 11],
 [2, 7, 6, -2, 3, 12],
 [7, -12, 2, 6, -3, -7]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[-9, 10, -2, 3, 14, -8],
 [3, 14, 15, -9, -2, -4],
 [13, 13, -6, -8, 0, -13],
 [-6, -14, -3, -9, 15, -7],
 [5, -11, -7, 15, -2, -9],
 [9, -8, -8, 6, 0, -5]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[-14, 0, -10, 14, 9, -8],
 [0, 9, 15, 11, -5, 13],
 [0, 0, -13, -6, 11, -11],
 [0, 0, 0, -1, -2, -15],
 [0, 0, 0, 0, 8, -4],
 [0, 0, 0, 0, 0, 12]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[-3, 4, -7, 0, -8, -2],
 [4, 8, 3, -4, 2, -10],
 [-7, 3, 2, 2, 3, -8],
 [0, -4, 2, -3, -2, 12],
 [-8, 2, 3, -2, -4, -2],
 [-2, -10, -8, 12, -2, -11]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[2, -6, 2, 1, -3, 4],
 [-6, 14, 0, 5, 4, 4],
 [2, 0, 10, 4, -1, 13],
 [1, 5, 4, 11, 3, -4],
 [-3, 4, -1, 3, -10, 0],
 [4, 4, 13, -4, 0, -7]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[-13, 0, -2, 7, -7, 8],
 [0, 3, -2, 2, 0, 4],
 [-2, -2, -4, -2, -4, 7],
 [7, 2, -2, -7, -2, -12],
 [-7, 0, -4, -2, 3, -6],
 [8, 4, 7, -12, -6, 0]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[-1, 13, 2, -5, -10, -1],
 [0, -1, -2, -1, 9, -6],
 [0, 0, -9, -1, 9, 12],
 [0, 0, 0, -12, 0, -10],
 [0, 0, 0, 0, 2, -8],
 [0, 0, 0, 0, 0, -5]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[3, 2, 14, 5, 2, -9],
 [-8, 2, 5, 0, 8, -2],
 [-5, -6, -7, -15, -8, 8],
 [9, -13, -3, -5, 8, -12],
 [-6, 14, -8, 5, -5, 9],
 [-4, -5, 0, 1, -9, 5]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[-15, -15, 6, 6, -13, 0],
 [-6, 8, 0, -8, 5, 4],
 [-3, -3, 12, 10, 7, 8],
 [-1, 14, 5, 9, -10, 1],
 [13, 11, -5, 8, 0, 12],
 [2, -5, 2, -7, -10, 4]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[-12, 9, -5, 13, 7, 11],
 [0, -2, -14, 5, 2, -13],
 [0, 0, -1, 0, 4, -15],
 [0, 0, 0, -4, 12, -10],
 [0, 0, 0, 0, 10, -5],
 [0, 0, 0, 0, 0, -13]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[2, -14, -9, 2, -5, 11],
 [14, 7, 6, 12, 13, 1],
 [-10, -14, 8, -13, 8, 13],
 [11, -3, -8, 5, 11, 7],
 [11, -14, 1, 6, 10, 4],
 [-7, 6, -13, -1, -9, 10]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[5, 7, 6, 10, 10, -10],
 [0, -11, 3, -4, 4, -2],
 [0, 0, 3, -9, -4, 14],
 [0, 0, 0, -1, -4, 13],
 [0, 0, 0, 0, 1, 9],
 [0, 0, 0, 0, 0, 14]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[-10, 6, -8, -8, 8, -14],
 [2, -1, -14, 11, -13, -12],
 [13, 15, 15, 0, -8, 13],
 [13, -11, 15, 3, 2, 14],
 [13, -6, -7, 12, 4, 14],
 [12, 7, -13, 10, -13, -5]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[6, 11, 2, 2, -1, 6],
 [11, 15, -4, 0, -6, 6],
 [2, -4, 4, 4, 2, -2],
 [2, 0, 4, 9, 1, -2],
 [-1, -6, 2, 1, -1, -6],
 [6, 6, -2, -2, -6, 14]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[-9, 2, -4, 6, -2, 4],
 [2, 11, 10, -4, 2, 2],
 [-4, 10, 4, -4, -1, 6],
 [6, -4, -4, -10, -4, -6],
 [-2, 2, -1, -4, -12, 0],
 [4, 2, 6, -6, 0, 5]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[0, 8, 3, 11, 1, 2],
 [15, 10, 14, -8, 13, 14],
 [-12, 6, 4, 8, 5, 13],
 [-12, 2, -7, -5, 7, -14],
 [1, -10, -2, -6, 5, 8],
 [14, 13, -3, -2, 0, -12]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[6, -7, 8, 2, -7, 8],
 [0, 14, -12, -10, 14, 9],
 [0, 0, 9, -11, 1, 0],
 [0, 0, 0, -4, 15, -3],
 [0, 0, 0, 0, 3, 3],
 [0, 0, 0, 0, 0, 11]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[-7, -11, 10, 1, 13, 2],
 [0, -4, 1, 10, 12, 1],
 [0, 0, -13, -15, -8, -8],
 [0, 0, 0, 3, -12, 3],
 [0, 0, 0, 0, -6, -13],
 [0, 0, 0, 0, 0, 10]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[11, 2, 8, -4, -1, 6],
 [2, 4, 4, -3, -2, -2],
 [8, 4, -5, 4, 0, -6],
 [-4, -3, 4, -11, -4, 14],
 [-1, -2, 0, -4, 12, 4],
 [6, -2, -6, 14, 4, -11]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[-5, 9, 5, -2, -4, -8],
 [0, 3, 7, -13, 3, 15],
 [0, 0, -14, -7, -7, -6],
 [0, 0, 0, -1, 7, 4],
 [0, 0, 0, 0, 13, 15],
 [0, 0, 0, 0, 0, -11]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[9, -5, -3, 10, -10, 7],
 [0, 2, -3, -7, 11, -9],
 [0, 0, -5, 1, -12, 14],
 [0, 0, 0, -14, 14, -13],
 [0, 0, 0, 0, 6, -6],
 [0, 0, 0, 0, 0, -3]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[-3, 2, 4, 8, -5, 14],
 [1, -1, -9, -4, 6, -2],
 [6, 12, -2, -9, 8, -5],
 [-2, 0, -4, 15, 10, -6],
 [1, 5, 4, 10, -3, 8],
 [-10, -5, 8, -13, 3, -3]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[12, -4, -14, 0, 8, 2],
 [-4, -2, -5, -4, -2, -2],
 [-14, -5, -14, 1, 0, 6],
 [0, -4, 1, -13, 3, -2],
 [8, -2, 0, 3, -13, -2],
 [2, -2, 6, -2, -2, 2]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[14, 6, 11, 4, -9, 11],
 [-11, 0, 11, -11, 9, 14],
 [3, -2, -3, 6, -8, 1],
 [-1, -5, -1, 9, -3, 14],
 [-7, 0, -11, 15, 13, 5],
 [9, 12, 10, 8, -5, -3]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[-12, 2, -9, -11, -6, -1],
 [2, -5, 6, 4, 5, -7],
 [-9, 6, -9, -4, -6, 8],
 [-11, 4, -4, -12, -10, 6],
 [-6, 5, -6, -10, -1, -4],
 [-1, -7, 8, 6, -4, 7]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[10, -10, -5, -3, 2, -3],
 [0, -6, -11, 12, 13, 15],
 [0, 0, -3, -7, 3, -5],
 [0, 0, 0, 3, -8, -3],
 [0, 0, 0, 0, 11, 4],
 [0, 0, 0, 0, 0, 4]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[-15, -11, 6, -15, -8, -12],
 [0, -5, -7, 15, 1, -3],
 [0, 0, 11, 4, 4, 5],
 [0, 0, 0, 5, 8, -2],
 [0, 0, 0, 0, 2, 1],
 [0, 0, 0, 0, 0, -6]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[10, -2, -12, -2, 6, -6],
 [-2, -12, 10, 4, 6, -3],
 [-12, 10, 2, -8, -4, 2],
 [-2, 4, -8, -1, 0, 9],
 [6, 6, -4, 0, 9, -6],
 [-6, -3, 2, 9, -6, -3]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[1, -2, -9, -3, 2, -12],
 [0, -13, -15, 14, 9, 9],
 [0, 0, 10, 7, -12, -7],
 [0, 0, 0, 15, 6, -6],
 [0, 0, 0, 0, 3, 6],
 [0, 0, 0, 0, 0, -4]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[-3, -10, -11, 9, 10, -11],
 [12, -10, 1, -3, -12, -9],
 [-13, -4, -10, -10, 10, 13],
 [-13, 3, -1, 2, -7, -5],
 [-9, 15, -7, -15, -14, 3],
 [-15, 7, -10, 2, 11, -8]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[-7, 10, 10, 2, 12, 2],
 [10, 7, -2, -6, -8, -4],
 [10, -2, -5, -2, -12, -5],
 [2, -6, -2, -2, -2, -4],
 [12, -8, -12, -2, -7, -4],
 [2, -4, -5, -4, -4, 1]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[-2, 6, 4, 3, -3, 8],
 [6, 2, 0, 0, 4, 6],
 [4, 0, -9, 3, 2, -10],
 [3, 0, 3, -11, 2, 0],
 [-3, 4, 2, 2, -2, -2],
 [8, 6, -10, 0, -2, 8]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[6, 8, -12, 3, 2, 3],
 [8, -6, 8, -8, -4, 0],
 [-12, 8, 4, 0, 4, -6],
 [3, -8, 0, 12, -6, 4],
 [2, -4, 4, -6, 12, -5],
 [3, 0, -6, 4, -5, 4]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[1, -9, -4, 0, -2, -6],
 [-9, -11, 4, -2, -2, 10],
 [-4, 4, 2, -1, 0, 2],
 [0, -2, -1, -13, -2, -2],
 [-2, -2, 0, -2, 8, 4],
 [-6, 10, 2, -2, 4, 14]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[3, -4, -6, 2, -11, 2],
 [-4, 5, -13, 2, 4, 8],
 [-6, -13, -12, -6, -7, -10],
 [2, 2, -6, 6, -7, -6],
 [-11, 4, -7, -7, 15, -8],
 [2, 8, -10, -6, -8, 8]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[-3, 8, 5, -10, 7, -2],
 [0, 2, -2, 9, -10, -14],
 [0, 0, 11, 8, -11, -12],
 [0, 0, 0, -10, 12, -7],
 [0, 0, 0, 0, -6, -11],
 [0, 0, 0, 0, 0, -13]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[-13, 2, -9, 11, -15, -13],
 [0, -1, -12, 4, -4, 14],
 [0, 0, -7, -4, -15, 3],
 [0, 0, 0, 2, 7, 4],
 [0, 0, 0, 0, 3, 14],
 [0, 0, 0, 0, 0, -5]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[-13, 4, -8, 10, -1, 11],
 [9, -9, 14, 2, 13, 5],
 [4, -5, 6, 8, -12, 0],
 [-11, 0, 2, -14, -14, -12],
 [15, -13, -15, -11, 7, -11],
 [-1, 3, -3, 7, 14, 7]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}