Idempotent Matrix Proof 1. The problem statement, all variables and given/known data Given a matrix A where A2 = A, find the properties of A. 2. Relevant equations detA = ai1ci1 + ai2ci2 + ... + aincin (where cij = (-1)i+j*detAij) aij = ai1a1j + ai2a2j + ... + ainanj 3. The attempt at a solution In order for A2 to be defined, A must be a square matrix. I have concluded that A must either equal the identity matrix I, or A must be singular. I am having trouble proving this in the general case.