When are two matrices A and B said to be...

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.

Verified by Experts

The correct Answer is:

A + B and AB are not defined; BA=`{:[(81,97),(16,20),(38,45)]:}`

Similar Questions

Explore conceptually related problems

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={:[(1,2,1),(1,-1,1),(2,3,-1)]and B={:[(1,4,0),(-1,2,2),(0,0,2)], find the matrix AB - 2B.

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

If A={:((3,2),(3,3))and B={:((1,-2/3),(-1,1)) show that AB=I_(2) where I_(2) is the unit matrix of order 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.

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 .

Find the matrices A and B for which: {:2A+B={:[(1,2,3),(-1,-2,-3),(4,2,3)] and A+2B={:[(0,2,3),(4,1,7),(1,1,5)]

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