 The inverse problem for the commutation relation "AK = KA" of identifying all involutory "K" that commute with a fixed matrix "A", has also been studied.Symmetric centrosymmetric matrices are sometimes called bisymmetric matrices.When the ground field is the field of real numbers, it has been shown that bisymmetric matrices are precisely those symmetric matrices whose eigenvalues remain the same aside from possible sign changes following pre or post multiplication by the exchange matrix.