If A is a symmetric and B skew symmetric matrix and `(A+ B)` is non-singular and `C = (A+B)^-1 (A-B)`, then prove that

If A is a symmetric and B skew symmetric matrix and (A+B) si non-singular and C=(A+B)^(-1)(A-B) , then prove that. (i) C^(T)(A+B)C=A+B (ii) C^(T)(A-B)C=A-B

If A is symmetric and B skew- symmetric matrix and A + B is non-singular and C= (A+B) ^(-1) (A-B) C^(T) AC equals to

If A is symmetric and B skew- symmetric matrix and A + B is non-singular and C= (A+B) ^(-1) (A-B) , C^(T)(A+B)C equals to

If A is a symmetric matrix and B is a skew-symmetric matrix such that A + B = [{:(2,3),(5,-1):}] , then AB is equal to

If A is a symmetric matrix and B is a skew-symmetric matrix such that A + B = [{:(2,3),(5,-1):}] , then AB is equal to

If A is a symmetric matrix and B is a skew-symmetric matrix such that A + B = [{:(2,3),(5,-1):}] , then AB is equal to

If A is a symmetric matrix and B is a skew-symmetric matrix such that A + B = [{:(2,3),(5,-1):}] , then AB is equal to

If A= B+C such that B is a symmetric matrix and C is a skew - symmetric matrix , then B is given by :

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

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