Cartesian Product is Small iff Inverse is Small

Theorem
Let $A$ and $B$ be classes.

Then the Cartesian product $A \times B$ is a small class iff $B \times A$ is small.

Proof
If $B \times A$ is a small class, then $A \times B$ is also small by Inverse is Small.

Similarly, if $A \times B$ is small, then so is $B \times A$, by the same statement above.