This is not a homework, this question came in my exam, and I did not know how to solve it.

"Let $A$ and $B$ be $3\times3$ matrices such that $AB = - BA$. Show that if $A$ is invertible, then $B$ is not invertible"

I tried starting with the expression $ AB = - BA$ and multiply $A$ by its inverse, but no luck.

Thank you!