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

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

If A = ((3,1),(0,2)) show that (A^(T))^(-1) = (A^(-1))^(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={:[(-2,1,3),(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={:[(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.

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

If A = (t^2,2t) and B = (1/t^2,-2/t) and S = (1,0), then show that 1/(SA)+1/(SB)=1

Let A and B be 3xx3 matrtices of real numbers, where A is symmetric, "B" is skew-symmetric , and (A+B)(A-B)=(A-B)(A+B)dot If (A B)^t=(-1)^k A B , where . (A B)^t is the transpose of the mattix A B , then find the possible values of kdot