We denote n×n Complex matrices by C^(n×n), let C^(n×n) be the space of complex n- tuples.For A∈C^(n×n), the symbols A^*, A^†, N(A),A^T,¯A, rank(A) and R(A)denote the conjugate transpose, Moore- Penrose inverse, Null space,transpose, conjugate,rank of A and Range space respectively. we denote the solution AXA=A by A^-. Let G be the unit perdiagonal matrix that has 1’s on the secondary diagonal and 0’s elsewhere. That is...