1. The problem statement, all variables and given/known data Given that q is an eigenvalue of a square matrix A with corresponding eigenvector x, show that qk is an eigenvalue of Ak and x is a corresponding eigenvector. 2. Relevant equations N/A 3. The attempt at a solution I really haven't been able to get far, but; If x is an eigenvector of A corresponding to q, then; 0=(A-qI)x To complete the proof I need to use this equation to show that (Ak-qkI)x=0, and this is where I'm having trouble. If anyone has time to help I would really appreciate it.