$A$ is a 2 × 3 matrix and $B$ is a 3 × 2 matrix. Which of the following statements are true?

I. $AB$ is defined, and its order is $2 \times 2$.

II. $BA$ is defined, and its order is $3 \times 3$.

III. $AB = BA$.

IV. $A + B$ is defined.

Explanation

1. 01

   Both products are defined, since the inner numbers match each way: $AB$ is $2 \times 2$ and $BA$ is $3 \times 3$.

2. 02

   Matrices of different orders cannot be equal, so III is false, and $A$ and $B$ have different orders, so $A + B$ is not defined.