Suppose matrix product AB is defined If A is a 31 times 16 m

Suppose matrix product AB is defined. If A is a 31 times 16 matrix and B is a column matrix, give the dimensions of B and AB. If A is an identity matrix and AB is 42 times 41, what size is matrix A? If A is 99 times 52 and AB is 99 times 72, what size is B?

Solution

to define the product the two matrices the column of first matrix should equal rows of second matrix

a) A is 31 x 16 , so to AB to be defined B must be 16 x 1, as B is column matrix

and then AB should be 31 x 1.

b) 42 x 42 , same reason

c) A is 99 x 52 and AB is 99 x 72 , so B must be 52 x 72.