Matrix calculator
A × B and B × A are generally different matrices, and often one of them does not even exist — a 2×3 can multiply a 3×2 but not the other way round. The inner dimensions have to match, and the result takes the outer ones. That non-commutativity is not a quirk; it is exactly what makes matrices useful for describing rotations, where doing two turns in a different order genuinely lands you somewhere else.
Enter matrices one row per line. Multiplication requires the columns of A to match the rows of B. The determinant exists only for square matrices, and a matrix is invertible only when its determinant is non-zero.
How to use the matrix calculator
The determinant has a geometric meaning that makes it far less abstract: it is the factor by which the matrix scales area in two dimensions, or volume in three. A determinant of 2 doubles areas; a determinant of −1 reflects without changing size; a determinant of zero collapses everything onto a line or a point, which is precisely why such a matrix cannot be inverted — the collapse destroys information that no operation can restore.
Questions
One row per line, values separated by spaces or commas. Every row must have the same length.