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 A is n x m and B is m x n, and if AB = In, then BA is an idempotent 2. Relevant equations 3. The attempt at a solution I have this one identity I think, but I'm not sure how to use it? If A is m x n, then ImA = A = AIn B*In*In*A can I do anything with that? My inverse definition shows for square matrices... how does it apply for non-square matrices? Or how can I use it?