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

If A and B are symmetric matrices then

If A, B are symmetric matrices of same order, then AB-BA is a

Let A and B two symmetric matrices of order 3. Statement 1 : A(BA) and (AB)A are symmetric matrices. Statement 2 : AB is symmetric matrix if matrix multiplication of A with B is commutative.

Let A be a square matrix. Then prove that (i) A + A^T is a symmetric matrix and, (ii) A -A^T is a 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 symmetric matrices of the same order, then show that AB is symmetric if and only if A and B commute i.e AB = BA .

If A, B are square materices of same order and B is a skewsymmetric matrix, show that A^(T)BA is skew-symmetric.

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

If A and B are matrices of the same order, then A B^T-B A^T is a (a) skew-symmetric matrix (b) null matrix (c) unit matrix (d) symmetric matrix

If A and B are non-singular symmetric matrices such that AB=BA , then prove that A^(-1) B^(-1) is symmetric matrix.