Hi guys, can you please help me out??

Question

A and B are nonsingular matrices and positive definite. Show that:

If $\displaystyle A-B>0$ , then $\displaystyle B^{-1}-A^{-1}>0$

What I have tried

I tried showing $\displaystyle B^{-1}-A^{-1}$ is a quadratic form but firstly I'm guessing that doesn't even show it's positive definite, only positive semi-definite. And secondly, I couldn't get it to work anyway.

Please help!!

Thanks!