4. (5 points) Suppose A is a k x k matrix such that A^n = 0, where n E N. Prove that A - Ik is invertible. Hint: you may

use the factorization technique x^{n}-a^{n}=(x-a)\left(x^{n-1}+x^{n-2} a+\cdots+x a^{n-2}+a^{n-1}\right)