Let A = [ jk ] be an n n matrix with (not necessarily distinct) eigenvalues

Let A = [α_jk] be an n × n matrix with (not necessarily distinct) eigenvalues λ₁, · · · , λ_n. Show.

A - kI has the eigenvalues λ₁ - k, · · ·, λ_n - k and the same eigenvectors as A.