$A$ and $B$ are both 3 × 2 matrices. Which of the products $AB$ and $BA$ is defined?

Explanation

1. 01

   $AB$ needs the columns of $A$ (2) to equal the rows of $B$ (3): they do not.

2. 02

   $BA$ needs the columns of $B$ (2) to equal the rows of $A$ (3): they do not either.