# Basic invertible matrix theorem proof.

If A and B are invertible matrices, can anyone prove that

(AB)^(-1) = B^(-1)*A^(-1) ?

This is not exactly the problem, I have, but my group theory problem is isomorphic to it :).

With that expression for $(AB)^{-1}$, does the following hold?
$$(AB)^{-1}(AB)=1$$