Find the product AB, if defined, when `A=[(1, 3), (2, 1)] and B=[(4),(-1)]`

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.

Find, where possible, A + B, A - B, AB and BA stating with reasons, where the operations are not pssible, when A={:[(4,2,-1),(3,-7,1)]:}and B={:[(2,3),(-3,0),(-1,5)]:}

Find AB, if A=[{:(1,2,3),(1,-2,3):}] and B=[{:(1,-1),(1,2),(1,-2):}] . Examine whether (AB)^(-1) exist or not.

(i) if A=[{:(1,-4),(3,1):}]and b=[{:(1,0,5),(-2,4,3):}], then show that : (AB)'=B'A' (ii) if A=[{:(2,3),(0,1):}]and B=[{:(3,4),(2,1):}], then prove that : (AB)'=B'A'

Find (AB)^(-1) if A=[(3,4),(1,1)] ,B^(-1)=[(4,3),(2,1)]

Find the product of 3ab^(2)and (4ab+3b^(2))

Find (AB)^(-1) if A=[(5,0),(2,3)] ,B^(-1)=[(1,2),(1,4)]

Find the product of (3a + 4b) and (3a - 4b) and verify it when a = -1 and b = 1 .

Of the matrices A=[(2,1,3),(4,1,0)] and B=[(1,-1),(0,2),(5,0)] Find AB , B^T , (AB)^T