Matrix inverse

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The inverse of a square matrix A is X if

(In 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.