Show that if a matrix A has an eigenvector x corresponding to the eigenvalue h, then x is also an eigenvector of the matix A^2 and state the corresponding eigenvalue.

Write an analogous result for A^n.

I'm afraid this kind of has me stumped. I have managed to do a couple of questions on eigenvalues and eigenvectors, but I can't apply that knowledge to this problem.

Anyone help?!?