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 X={:[(1,-3,-4),(-1,3,4),(1,-3,-4)], show that, X^(2)=0 where 0 is the null matrix of order 3xx3.

If A={:[(1,1,-1),(2,-3,4),(3,-2,3)]and B={:[(-1,-1,1),(2,2,-2),(-3,-3,3)] , prove that ABne0 but BA = 0.

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={:[(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.

|{:(1,-3,2),(4,-1,2),(3," "5,2):}|

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.

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.

|{:(1,3,5),(2,4,3),(4,6,7):}|

If A={:[(2,-3),(0,1),(-1,4)],B={:[(-1,5),(2,-3),(0,1)],C={:[(4,-2),(0,-1),(3,5)], Find the matrices A+2B

If A=[{:(2,3,-1),(1,4,2):}] and B=[{:(2,3),(4,5),(2,1):}] then prove that AB and BA are not equal.