Let A denote an n n matrix and put A1 = A - I, in

Let A denote an n × n matrix and put A1 = A - αI, α in R. Show that λ is an eigenvalue of A if and only if λ - α is an eigenvalue of A1. How do the eigenvectors compare? (Hence, the eigenvalues of A1 are just those of A "shifted" by α.)