Prove that if is an eigenvalue of a matrix A with associated eigenvector x, and k is a positive integer, then k is an eigenvalue of the matrix Ak A ( A A (k factor) With associated eigenvector x

Question: Prove that if is an eigenvalue of a matrix A with associated eigenvector x, and k is a positive integer, then k is an

Prove that if λ is an eigenvalue of a matrix A with associated eigenvector x, and k is a positive integer, then λk is an eigenvalue of the matrix
Ak = A ( A ...... A (k factor)
With associated eigenvector x?

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