Decomposition of positive definite matrix.

Question

Let $A$ be a positive definite matrix. Following are the decomposition's of matrix $A$:

1. $A = PP$
2. $A = MM^{T}$

Empirically we found that $||P||_{F}^2 = ||M||_{F}^2$ but how to prove this analytically? Here $||\cdot||_{F}$ denotes the Frobenius norm.