Let A ∈ R^(n×n)be a matrix with characteristic polynomial
λ(s)=det⁡(sI-A)=s^n+a_1 s^(n-1)+...+a_(n-1) s+a_n.
Assume that the matrix A can be diagonalized and show that it satisfies
λ(A)=A^n+a_1 A^(n-1)+...+a_(n-1) A+a_n I=0,
Use the result to show that A^k,k≥n, can be rewritten in terms of powers of A of order less than n.

A^n+a_1 A^(n-1)+⋯+a_(n-1) A+a_n I=0を使ってA^k=の式を示すところが分からないので教えてほしいです