In this exercise A is a square matrix.

1) Show that if A^2 = 0 then (A - I) is invertible.

2) Show that if A^3 = 0 then (A - I) is invertible.

3) Show that if A^4 = 0 then (A - I) is invertible.

4) Assume that there is a natural number k such that A^k = 0. Prove that (A - I)