Show that if \(\displaystyle \left\|P \right\|_2 = 1, \) then P is an orthogonal projection.

I know that for any projection P, \(\displaystyle \left\|P \right\|_2 \geq 1, \) , and that if P is an orthogonal projection, then \(\displaystyle \left\|P \right\|_2 = 1, \), but I am not sure how to prove the other way around.