Matrix Calculator

Matrices, With the Working

Find determinants and inverses or multiply two matrices, with every row operation and dot product written out. Enter integers, decimals or fractions like 3/4 — answers stay exact.

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Examples:

Quick facts

Determinant. A single number that tells you how the matrix scales area or volume. If it is 0, the matrix squashes space flat and has no inverse.

Inverse. The matrix that undoes A, so A × A⁻¹ = I. It exists only for square matrices with a non-zero determinant.

Multiplication. Row-by-column dot products. The order matters — A × B is usually different from B × A.