Matrix multiplication

Question

For the following matrices show that AB ≠ BA or that at least one of the products does not exist:

 

A=[[-1,0],[2,3]]   B=[[2],[0]]

Answer 1

A is a 2x2 matrix.

B is a 1x2 matrix.

 

BA is defined, because you can multiply a (1x2) matrix by a (2x2) matrix, in that order, and get a (1x2) matrix.

 

AB is not defined, because you cannot multiply a (2x2) matrix by a (1x2) matrix, in that order.