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,-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={:[(2,0,9),(-1,6,10),(4,-1,2)]:},B={:[(0,-1,-2),(3,2,-1),(4,-2,0)]:} and C={:[(1,-2,0),(0,1,2),(3,0,-1)]:} then show that, A(B+C) = AB + AC.

If A={:[(2,0,9),(-1,6,10),(4,-1,2)]:},B={:[(0,-1,-2),(3,2,-1),(4,-2,0)]:} and C={:[(1,-2,0),(0,1,2),(3,0,-1)]:} then show that, A(BC) = (AB)C

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

Let A+2B=[(1,2,0),(6,-3,3),(-5,3,1)] and 2A-B=[(2,-1,5),(2,-1,6),(0,1,2)], then find tr(A)-tr(B).

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 = [{:(1,0,1),(0,1,2),(0,0,4):}] , then show that |3A|=27|A|.