Verify that `(AB)^(T)=B^(T)A^(T),` where
`A={:[(1,2,3),(3,-2,1)]and B={:[(1,2),(2,0),(-1,1)]`.

For the matrices A and B, verify that (AB)'=B'A' , where (i) A=[(1),(-4),(3)], B=[(-1,2,1)] (ii)A=[(0),(1),(2)],B=[(1,5,7)]

Determine the matrices A and B, where A+2B={:[(1,2,0),(6,-3,3),(-5,3,1)] and 2A-B={:[(2,-1,5),(2,-1,6),(0,1,2)]:} .

Find, where possible, A + B, A - B, AB and BA stating with reasons, where the operations are not pssible, when A={:[(4,2,-1),(3,-7,1)]:}and B={:[(2,3),(-3,0),(-1,5)]:}

If A={:[(1,1),(2,2),(3,3)], find "AA"^(T).

If A={:[(1,2,1),(1,-1,1),(2,3,-1)]and B={:[(1,4,0),(-1,2,2),(0,0,2)], find the matrix AB - 2B.

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.

If A=[(1,2,3),(2,1,2),(2,2,3)]B=[(1,2,2),(-2,-1,-2),(2,2,3)] and C=[(-1,-2,-2),(2,1,2),(2,2,3)] then find the value of tr. (A+B^(T)+3C) .

If A=[(-1,2,3),(5,7,9),(-2,1,1)] and B=[(-4,1,-5),(1,2,0),(1,3,1)] , then verify that (i) (A+B)'=A'+B' , (ii) (A-B)'=A'-B'

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,-3),(5,0,2),(1,-1,1)],B=[(3,-1,2),(4,2,5),(2,0,3)] and C=[(4,1,2),(0,3,2),(1,-2,3)] , then compute (A+B) and (B-C) . Also, verify that A+(B-C)=(A+B)-C .