Matrix inverse

In matrix algebra, the inverse of a square matrix A is X if

$\mathbf {AX} =\mathbf {XA} =\mathbf {I} _{n}\$

(I_n is the n-by-n identity matrix). If this equation is true, X is the inverse of A, denoted by A^-1 ( and A is the inverse of X). Furthermore, the inverse X is unique (if Y were also an inverse consider X.A.Y).

A matrix is invertible if and only if it possesses an inverse. The inverse may be computed from the adjugate matrix, which shows that a matrix is invertible if and only if its determinant is itself invertible: over a field such as the real or complex numbers, this is equivalent to specifying that the determinant does not equal zero.