Prove orthogonal projections for a matrix A and its transpose

Question

I'm trying to prove that a projection is orthogonal using: $A ∈ \mathbb R^{m\times n} $ where $A^TA = I_n$, and I want to prove that $P=AA^T$ is an orthogonal projection.

I understand that an instance where $A^TA = I_n$ implies orthogonality, but what is the proof here?