I am studying for finals and am looking over previous problems that I missed significant points on. My instructor doesn't comment on why things are incorrect and he doesn't discuss homework, so I am on my own to figure out why I am wrong. Anyway, I would like some help figuring out where I went wrong.

Theorem:

If matrices such that , then are invertible. Furthermore, we have

Problem:

Show that if then

Proof:

By the theorem above we have

Which doesn't seem to get me anywhere. Any help is appreciated. Thank you in advance.