The sizes of two matrices A and B are given.

Question

Find the sizes of the product AB and the product​ BA, whenever these products exist.

A is 4x2, and B is 2x4

Answer 1

We are given two matrices and their respective sizes...

A = 4x2

B = 2x4

The rules for matrix multiplication are that the outer left and outer right dimensions of the two matrices must match and the inner right and inner left dimensions of the two matrices determine the resultant size.

In our case here...

AB = (4x2) (2x4)

We see the (outer) 4 from A = the (outer) 4 from B. Therefore the inner, remaining, dimensions will express the result matrix.

AB = (4x2) (2x4) yields a 2x2 matrix result

BA = (2x4) (4x2) yields a 4x4 matrix result

Both products exist.