Adjoint matrix

The adjoint matrix is defined as the transpose of the cofactor matrix. Given a matrix A of dimensions n cross times n, the cofactor matrix C is the matrix whose left parenthesis i comma j right parenthesis entry is the left parenthesis i comma j right parenthesis cofactor of A: C subscript i j end subscript equals left parenthesis negative 1 right parenthesis to the power of i plus j end exponent M subscript i j end subscript, where M subscript i j end subscript denotes the left parenthesis i comma j right parenthesis minor of A. Thus, the adjoint matrix of A is a d j left parenthesis A right parenthesis equals C to the power of T.

adjoint_matrix(Matrix)

Given a matrix, computes its adjoint matrix.