1. The problem statement, all variables and given/known data A square matrix P is called an idempotent if P^2 = P, Show that if P is an idempotent, so is Q = (P + AP - PAP) for any square matrix A (of the same size as P). 2. Relevant equations 3. The attempt at a solution basically I factor, Q = (I + (I - P) A) P then I square it and try to get back to the original,... and end up with Q^2 = (I + (I - P - P + P^2) A^2) P^2 = (I + (I -2P + P) A^2) P = (I + (I - P) A^2) P = (I + AA - PAA) P = P + AAP - PAAP how do i get rid of the AA (A^2) ..?