How to prove that an orthogonal projection matrix is idempotent

[TheBuddha11]

Homework Statement

Prove that [P]^2=[P] (that the matrix is idempotent)

Homework Equations

The Attempt at a Solution

A(A^T*A)^-1 A^T= (A(A^T*A)^-1 A^T)^2

Where A^T is the transpose of A. I have no idea.

 

[D H]

What is the relationship between your matrix A and your matrix P?

Backing up a bit further, what is the definition of an orthogonal projection matrix?