Matrix Calculator

Matrix multiplication pairs each row of A with each column of B: the top-left entry is (row 1 of A)·(column 1 of B). Order matters — A×B and B×A usually differ — which encodes the fact that transformations applied in different orders give different results.

For a 2×2 matrix, ad − bc measures how the transformation scales area. Zero means the matrix flattens the plane onto a line — information is lost, so no inverse exists. The inverse formula swaps the diagonal, negates the off-diagonal, and divides by the determinant.