Positive semi definite matrix

Question

Let $C \in M_n(\mathbb R) $. We know that $C^T C$ is positive semi definite and symmetric. Let $D\in M_n(\mathbb R)$, such that $D^2 = C^TC$. Show that $\exists P \in M_n(\mathbb R)$ with $P^{-1} = P^T$, such that $C = PD$