If $T\in M_{n\times n}(\mathbb R)$ invertible, why is $T^tT$ positive definite?

Question

Let $T\in \mathcal M_{n\times n}(\mathbb R)$ invertible, why is $T^tT$ positive definite?

My only idea is $$x^tT^tTx=(Tx)^t(Tx)=\|Tx\|^2,$$ and since $T$ invertible $\|Tx\|=0$ only if $x=0$, but I don't think it's a good argument.