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Matrix inverse

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The inverse of a square matrix A is X if

\mathbf{AX} = \mathbf{XA} = \mathbf{I}_n \

(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).

A matrix is invertible if and only if its determinant does not equal zero.

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