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

If A={:[(0,1,2),(1,2,3),(3,1,1)]and B={:[(2,1,3),(-1,0,1),(3,-1,4)], show that, AB ne BA .

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={:[(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=[[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={:[(2,0,-5),(-3,4,7)] and B={:[(3,1,-1),(4,5,0)] then prove that (A+B)'=A'+B' (A-B)'=A'-B

If A={:[(0,2,3),(2,1,4)]andB={:[(7,6,3),(1,4,5)] , find 2A+3B.

If A={:[(2,-3,-5),(-1,4,5),(1,-3,-4)]:} and B={:[(-1,3,5),(1,-3,-5),(-1,3,5)]:} show that AB = BA = 0, where 0 is the zero matrix of order 3xx3 .

If A = ((3,1),(0,2)) show that (A^(T))^(-1) = (A^(-1))^(T) where A^(T) is the transpose of A .

When are two matrices A and B said to be conformable for the product AB? If A={:((1,2,3),(1,3,3),(1,2,4))and B={:((6,-2,-3),(-1,1,0),(-1,0,1)) show that, AB = BA. Is it, in general, true for matrix multiplication? Give an example to justify your answer.

If A={:[(1,-2,2),(0,1,-1),(0,0,1)]:} and B={:[(1,2,0),(2,3,-1),(0,-1,-2)]:}, then show that, (A'B)A is a diagonal matrix.