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

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, then compute (A+B) (A-B) .

If A and B are square matrices of order 2, then find (AB)^(T)-B^(T)A^(T) .

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

If BD and CE are two altitudes of triangleABC ,prove that (CA)/(AB)=(CE)/(DB)

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.

Verify with square matrices of order 2: (AB)'=B'A'

Prove that a matrix which is symmetric as well as skew-symmetric is a null matrix.

Give examples to show that : AB=BA

P and Q are respectively the base and the vertex of the tower PQ.AB is another tower which is at a certain distance apart from PQ.The height of AB is less than that of PQ and the base of AB is A.The angles of elevation of Q from A and B are respectively 60^@ and 45^@ .If AB=40m,find PQ,QA and QB.