Show that the inverse A1 exists if and only if none of the eigenvalues 1, , n

Show that the inverse A–1 exists if and only if none of the eigenvalues λ1, ∙ ∙ ∙, λn of A is zero, and then A–1 has the eigenvalues 1/ λ1, ∙ ∙ ∙, 1/λn.