For the matrices A and B, verify that `(AB)'=B'A'`, where
`(i) A=[(1),(-4),(3)], B=[(-1,2,1)] (ii)A=[(0),(1),(2)],B=[(1,5,7)]`

Verify that (AB)^(T) = B^(T) A^(T) if A= [(2,3,-1),(4,1,5)] and B= [(1,-2),(3,-3),(2,6)]

Matrices A and B will be inverse of each other only if

Verify (AB)^(-1)=B^(-1)A^(-1) with A=[{:(0,-3),(1,4)],B=[(-2,-3),(0,-1):}]

Verify the property A(B+C) = AB+AC, when the matrices A,B, and C are given by A=[(2,0,-3),(1,4,5)],B=[(3,1),(-1,0),(4,2)],and C=[(4,7),(2,1),(1,-1)] .

Verify (AB)^(-1)= B^(-1) A^(-1) for A = [(2,1),(5,3)] and B= [(4,5),(3,4)] .

A and B be 3xx3 matrices such that AB+A=0 , then

Find the slope of bar(AB) , where A(2, 1), B(2, 6)

If the matrices, A, B and (A+B) are non-singular, then prove that [A(A+B)^(-1) B]^(-1) =B^(-1)+A^(-1) .

If A and B are square matrices such that AB = BA then prove that A^(3)-B^(3)=(A-B) (A^(2)+AB+B^(2)) .