1. The problem statement, all variables and given/known data Prove that if A is an n x n matrix with the property A3=A, then det(A)=-1, det(A)=0, or det(A)=1 2. Relevant equations 3. The attempt at a solution At first I started with the property A3=A I then applied the determinant to both sides. From this point I don't really see any properties that I can use to solve this equation for the det(A). I understand how the solutions work. Im just unsure on how to achieve the proof of those solutions to the property. Am I missing something simple here?