If A and B are symmetric matrices, prove that `AB-BA` is a skew symmetric matrix.

If A and B are symmetric matrices then ABA is

If A and B are two symmetric matrices then AB + BA is

Let A and B be two symmetric matrices of order 3. Statement: 1: A(BA) and (AB)A are symmetric matrices. Statement: AB is symmetric if matrix multiplication of A with B is commutative.

If A, B are symmetric matrices of the same order then show that AB-BA is skew symmetric matrix.

If A and B are symmetric matrices of the same order, then show that AB is symmetric if and only if A and B commute, that is AB = BA.

If A and B are two skew symmetric matrices of order n then

For the matrix A=[(1,5),(6,7)] , verify that (i) (A+A') is a symmetric matrix (ii) (A-A') is a skew symmetric matrix