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={:[(2,1),(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^TA^T were A^T is the transpose of A.

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

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=1/3({:(-1,2,-2),(-2,1,2),(2,2,1):}) , show that "AA"^(T)=I_(3) .

If A = ((2,1),(3,4)) and B = ((1,-2),(-1,1)) show that, (AB)^(-1) = B^(-1) A^(-1)

If A=[(1,-2,3),(-4,2,5)] and B=[(2,3),(4,5),(2,1)] , then find AB, BA. Show that AB ne BA .

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