We denote by M(F) the set of all n×m matrices over the field F and by M(F) the set of all n×n matrices over the field F. W. E. Roth has shown the following theorem in 1952, [1]. Theorem Let A∈M(F),B∈M(F) and C∈M(F), then the matrix equation AX-YB=C (1) has a solution X, Y∈M(F) if and only if the matrices