Adjoint Matrix and Inverse Matrix of Semi-Magic Squares

Abstract

A semi-magic square is a square matrix whose row and column sums are all equal to the same constant m. In this paper, we prove that if A is a semi-magic square whose the sum is m ≠ 0 and det (A)  ≠ 0, then adj (A) and A^-1 are semi-magic squares whose the sum are and  , respectively.