If A is a 2 `xx` 3 matrix and AB is a 2 `xx` 5 matrix, then B must be a

Options

A. `3 xx 5` matrix
B. `5 xx 3` matrix
C. `3 xx 2` matrix
D. `5 xx 2` matrix

Answer

A

Explanation

A is 2 `xx` 3 matrix
AB is 2 `xx` 5 matrix
Let 'B' be m `xx` n matrix
`[A]_(2 xx 3) [B]_(m xx n) = [AB]_(2 xx 5)`
number of columns of A = number of rows of B
`therefore m = 3`
we can observe that n = 5 from the product.
So, B is 3 `xx` 5 matrix.