Proof for inverse matrices

Prove that for three non-singular matrices **A, B, C** that $\displaystyle (ABC)^{-1}=C^{-1}B^{-1}A^{-1}$

I know that for two square matrices, **C, D**, say, $\displaystyle (CD)^{-1}=D^{-1}C^{-1}$. I tried using this result to prove $\displaystyle (ABC)^{-1}=C^{-1}B^{-1}A^{-1}$, by considering **AB** as one square matrix, and multiplying by **C**, and here is my problem.

$\displaystyle (AB)^{-1}=B^{-1}A^{-1}$, I don't know how to continue after this. Or am I off the right track?

Thanks!