If `A={:((2,3),(6,5)):}and B={:((3,7),(4,0)):}` , express `(A+B)^(2)` as a matrix and show that, `(A+B)^(2)=A^(2)+AB+BA+B^(2)`.

If A={:((2,4),(5,6))and B={:((3,6),(5,9)), find the square matrix X of order 2xx2 such that, 3A + 4B = 2x.

If A={:[(2,-1),(3,2)]:} and B={:[(0,4),(-1,7)]:}, find 3A^(2)-2B+I

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.

If A={:[(0,2,3),(2,1,4)]andB={:[(7,6,3),(1,4,5)] , find 2A+3B.

If A = [{:(2,5),(2,1):}] and B = [{:(4,-3),(2,5):}] ,verify that |AB|=|A||B|.

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

If A={:((1,-3,4,2),(0,5,-2,3))and B=((-5,0,6,4),(7,8,-2,5)), find a matrix X of order 2xx4 such that 3A-2X=B.

If A={:((1,2),(-1,-2))and B={:((-1,3),(-3,1)). then show that, (A+B)^(2)ne A^(2)+2AB+B^(2).

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