1. The problem statement, all variables and given/known data to prove : square of density matrix= the density matrix itself (for a pure ensemble) 2. Relevant equations density matrix=sum over P(i) ket(i) bra(i) where Pi = probability that random chosen system from ensemble shows state i. summed over i , where P=1 for pure ensemble 3. The attempt at a solutioni thought it is giving the identity matrix, whose square is also I , hence the proof. but i am not sure about this.