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

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


[User]
Determine the value of det(A) where A =
[[-1, 0, -6, -4, 1, -2],
 [0, 3, 6, -6, 2, -2],
 [-6, 6, 9, 4, 10, -5],
 [-4, -6, 4, -11, 10, -11],
 [1, 2, 10, 10, -1, 3],
 [-2, -2, -5, -11, 3, 3]]
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:
[[2, 0, -12, 12, -8, -8],
 [0, 1, 2, -14, 0, 0],
 [-12, 2, -6, -4, -3, -8],
 [12, -14, -4, -4, 1, -6],
 [-8, 0, -3, 1, 8, -4],
 [-8, 0, -8, -6, -4, 15]]? 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:
[[-9, 14, 13, -2, -12, -8],
 [0, 3, 2, -3, 6, 13],
 [0, 0, -8, 4, -9, 15],
 [0, 0, 0, -4, 2, -6],
 [0, 0, 0, 0, 1, -3],
 [0, 0, 0, 0, 0, 8]]

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


[User]
Compute |A| for the matrix A =
[[7, 10, 3, 1, -11, -12],
 [0, -11, -9, 12, -3, 12],
 [0, 0, -13, -11, 13, 0],
 [0, 0, 0, 2, -1, -4],
 [0, 0, 0, 0, 9, -12],
 [0, 0, 0, 0, 0, 4]]
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 =
[[12, 9, -3, 14, -4, 13],
 [0, 1, -7, -13, 0, 13],
 [0, 0, -11, 4, 5, -7],
 [0, 0, 0, 7, 2, 15],
 [0, 0, 0, 0, 6, -3],
 [0, 0, 0, 0, 0, 6]]
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, 9, -6, -5, 7, -4],
 [0, 6, 6, -11, 5, -15],
 [0, 0, -11, -12, 11, 15],
 [0, 0, 0, 6, 12, 13],
 [0, 0, 0, 0, -3, -15],
 [0, 0, 0, 0, 0, 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]
Determine the value of det(A) where A =
[[-3, -11, -6, -1, -10, -8],
 [0, 14, 10, 13, 8, -10],
 [0, 0, 9, 8, -15, 14],
 [0, 0, 0, 14, 0, 0],
 [0, 0, 0, 0, 12, -2],
 [0, 0, 0, 0, 0, 3]]
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:
[[-5, 4, 10, -3, -14, 1],
 [2, 8, -1, -7, 8, 3],
 [-3, -1, 14, -13, 2, -10],
 [-6, 2, 2, 0, -1, 2],
 [-13, -11, -12, 0, -10, 8],
 [-2, 10, -8, -8, 4, -6]]

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


[User]
What is the determinant of the matrix:
[[13, -11, 8, 15, 0, -1],
 [0, 6, -4, 2, -14, 6],
 [0, 0, 11, 6, -15, 7],
 [0, 0, 0, 3, 13, 4],
 [0, 0, 0, 0, 1, 2],
 [0, 0, 0, 0, 0, 12]]? 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 =
[[5, -12, -9, 5, 6, 10],
 [0, 7, 7, 8, 4, -12],
 [0, 0, -10, 10, 11, -12],
 [0, 0, 0, -5, -9, 6],
 [0, 0, 0, 0, -3, 2],
 [0, 0, 0, 0, 0, -4]]
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 =
[[2, -4, -14, -11, 10, -7],
 [-13, -6, 11, 12, -11, -7],
 [-6, -10, -6, 0, -4, -13],
 [4, 15, -7, 15, -7, -4],
 [0, -14, 0, 6, -6, -9],
 [-2, -8, 11, 15, 1, 2]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

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