Matrix inverse

The inverse of a square matrix A is X if

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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. A matrix is invertible if and only if its determinant is itelf invertible: over a field such as the real or complex numbers, this is equivalent to specifying that the determinant does not equal zero.