When is matrix multiplication defined?

A(m×n) × B(n×p) works when A columns = B rows. Result is m×p.

What does the determinant mean?

The determinant represents scaling factor of the linear transformation. det=0 means the matrix is singular (not invertible).

Transpose flips rows and columns. Element a_ij becomes a_ji.

Last Updated: April 13, 2026

Free matrix calculator. Add, multiply, find determinant & transpose of 2x2 and 3x3 matrices.

Matrix A (2×2)

Matrix B (2×2)

📐 How We Calculate — Learn about our calculation methodology, data sources, and quality standards.