[" 12.If "A" is a symmetric,then show that "Lis3" as "AB" ,is "],[" symmetric matix."]

If A is a skew -symmetric matrix , then show that A^(2) is a symmetric matrix .

If A is symmetric , then show that B' AB is symmetric matrix .

If A is symmetric, show that B' AB is symmetric.

If A and B are symmetric matrices, then prove that AB +BA is a symmetric matrix.

If A and B are square matrices of the same order and A is symmetric, then show that B^t AB is also symmetric.

If A and B are symmetric matrices , then prove that AB+ BA is a symmetric matrix .

For, a 3xx3 skew-symmetric matrix A, show that adj A is a symmetric matrix.

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

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

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