Let $\displaystyle A, B$ be square matrices of order $\displaystyle n$.

If $\displaystyle A$ or $\displaystyle B$ is invertible, show that $\displaystyle AB$ is similar to $\displaystyle AB$.

First I saw this question, I think there' s a typo in this question since every matrix is similar to itself.

May be it should be $\displaystyle AB$ similar to $\displaystyle BA$.

Anyway, i still can't solve it if it is $\displaystyle BA$.