n. the matrix inverse to a given matrix with respect to matrix multiplication. When A is real or complex, A^-|, exists precisely when A is non-singular , and it is then computable by Gaussian elimination (in practice), or (in principle) by the adjugate formula
A^-| = (adj A) / det(A);
that is, the transpose of the matrix of the quotients of its cofactors by its determinant. See also Cramer's rule.