Basic invertible matrix theorem proof.

[Evil Robot]

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 :).

 

[Galileo]

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

$$(AB)^{-1}(AB)=1$$