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

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

If A=[(1,5),(6,7)] , verify that A+A' is a symmetric matrix and A-A' is a skew-symmetric matrix.

Express the matrix A as the sum of a symmetric matrix and a skew-symmetric matrix, where A=[(2,4,-6),(7,3,5),(1,-2,4)]

If A and B are two matrices such that AB =B and BA =A, then find the value of A^(2)+B^(2) .

If A and B are square matrices of order 3 such that |A| = -1 and |B| = 3, then find the value of |3AB|.

If A and B are square matrices of the same order, then compute (A+B) (A-B) .

Express [(2,3,4),(5,6,-2),(1,4,5)] as the sum of a symmetric matrix and a skew-symmetric matrix.

Give examples to show that : AB is a null matrix, where neither A nor B is a null matrix.

Prove tha tany square matrix can be expressed uniquely as the sum of a symmetric and a skew-symmetric matrix.

If A and B are two square matrices such sthat AB =BA, express (A+B)^(2)-A^(2)-B^(2) in terms of A and B.