< Mentor Note -- thread moved to HH from the technical math forums, so no HH Template is shown > Let A be a square matrix of order n such that A^2 = I a) Prove that if -1 is the only eigenvalue of A, then A= -I b) Prove that if 1 is the only eigenvalue of A, then A= I c) Prove that A is diagonalizable. For part a and b, I consider A=-I and I then showed that the eigenvalues are -1 and 1 respectively. Is it valid by assuming A=-I and I then proving the eigenvalues are -1 and 1? If A=-I, Av=λv -v=λv therefore, λ=-1. For part c, I have no clue how to even start. I did some research, and I haven't learn minimal polynomial so I can't use it to prove.