Proving positive definiteness of inner product

Question

If M is a real, invertible n x n matrix, how do I show that ${\langle a,b\rangle}=a^TM^TMb$ defines an inner product ($a$ and $b$ are column vectors in $\mathbb{R}^n$). I've proven that it satisfies the linearity and symmetry axioms, but I'm struggling to prove the positive definiteness axiom, where I need to prove that ${\langle a,a\rangle} > 0\ {\text{ if }}a\neq \mathbf {0}$.