If `A={:[(-1),(2),(3)]:} and B=[-2" "-1" "-4]` then verify that `(AB)^(T)=B^(T)A^(T).`

If A={:[(2,1),(3,4)]:} and B={:[(1,-2),(-1,1)]:} verify that, (AB)^(T)=B^(T)A^(T) where A^(T) is the transpose of A.

If A= {:[( 2,3),( 1,-4) ]:}and B = {:[( 1,-2),( -1,3) ]:} ,then verify that (AB)^(-1) =B^(-1) A^(-1)

If A = [(-3,-4),(4,5)] and B = [(2,-3),(5,-8)] , verify that (AB)^(-1) = B^(-1)A^(-1) .

If A'=[(3,4),(-1,2),(0,1)] and B=[(-1,2,1),(1,2,3)] , then verify that (i) (A+B)' =A'+B', (ii) (A-B)'=A'-B'

Let A= {:[( 3,7),( 2,5) ]:} and B = {:[( 6,8),( 7,9) ]:} .Verify that (AB) ^(-1) =B^(-1) A^(-1)

If A={:[(1,2,5),(-1,3,-4)]:} and B={:[(3,-2,1),(0,-1,4),(5,2,-1)]:}, show that, (AB)^(T)=B^(T)A^(T) where A^(T) is the transpose of A.

If A = [{:(2,5),(2,1):}] and B = [{:(4,-3),(2,5):}] ,verify that |AB|=|A||B|.

If A=[(-2),(4),(5)],B=[(1,3,-6)] , verify that (AB)'=B'A' .

If A=[[1,2,5].[-1,3,-4]] and B= [[3,-2,1],[0,-1,4],[5,2,-1]] show that (AB)^T=B^TA^T were A^T is the transpose of A.

If A={:[(1,-1,0),(-1,2,1),(0,1,1)]and B ={:[(1,1,-1),(0,1,-1),(0,0,1)] show that B^(T)AB is a diagonal matrix, where B^(T) is the transpose of B.