Question

suppose that y is an eigenvalue of matrix A with corresponding eigenvector X.Then if K is a +integer Y^k is an eigenvalue of the matrix A^k with corresponding eigenvector X.

Answer 1

recall:
AX=YX
(A^K)X=A^(K-1)(AX)
" =A^(K-1)(YX)
=YA^(K-2)(AX)
=YA^(K-2)(YX)
=Y^(K-1)(AX)
=Y^(K-1)(YX)
=Y^K(X)

Answer 2

What were you trying to do/ prove?