The **inverse** of a square matrix *A* is a second matrix such that *AA ^{-1} = A^{-1}A = I*,

*I*being the identity matrix. There are many ways to compute the inverse, the most common being multiplying the reciprocal of the determinant of

*A*by its adjoint (or adjugate, the transpose of the cofactor matrix). For example,

This is indeed the inverse of *A*, as

A matrix is invertable if and only if the determinant is not equal to zero.

## Pseudoinverse

The inverse of a matrix is normally defined for square matricies. For non-square matrix, a corresponding pseudoinvere matrix can be constructed to produce an identity matrix.