kλ is an eigenvalue of kA for any real number k because if λ is an eigenvalue of A, with eigenvector x, then kAx = kλx so x is also an eigenvector of kA with eigenvalue kλ. Similarly, λ^n is an eigenvalue of A^n, where n is a positive integer, because if Ax = λx then applying A repeatedly n times gives A^nx = λ^nx, so x is an eigenvector of A^n with eigenvalue λ^n.