proof question:

A linear operator E on a vector space V is called idempotent if E2 = E (here E2 = E o E). If V is a nite-dimensional inner product space, is every orthogonal projection mapping onto a subspace idempotent? Is every idempotent linear operator on V an orthogonal projection mapping onto some subspace? For each of these two questions, prove it if the answer is yes, and give a counterexample if the answer is no