data/knowledge_base/linear_algebra.md

Linear Algebra – Basics

Matrix Addition

Possible only if matrices have same order

Matrix Multiplication

• Order matters (AB ≠ BA)
• Columns of A must match rows of B

Determinant (2×2)

|a b| |c d| = ad − bc

Inverse Exists If

det(A) ≠ 0

Common Mistakes

• Multiplying matrices in wrong order
• Using inverse when determinant is zero