Hi, I have the following problem with an idempotent matrix and I am stuck...

If A is an idempotent (A^2 = A), is E - nA invertible /E is the identity matrix and n is a real number/ and why?

I've tried with setting (E - nA)(E - nA) but it doesn't get me anywhere..

My instinct is telling me there it should be invertible in a lot of the cases, but... :/