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

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

If A is a matrix of order 3xx4 and B is a matrix of order 4 xx5 then what is the order of the matrix (AB)^(T) ?

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

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

Verify with square matrices of order 2: A(B+C)=AB+AC

Verify with square matrices of order 2: A(BC)=(AB)C

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