1. The problem statement, all variables and given/known data Let A be an nxn matrix such that A^k=0 for some natural integer k (0 is the nxn zero matrix). Show that I + A is invertible, where I is the nxn identity matrix. 2. Relevant equations Invertible implies det(I+A) not equal zero. 3. The attempt at a solution I really don't know where to start with this one. I can see that A itself must be non-invertible, but I can't seem to get any more conditions on A based on that fact that A^k=0. Could anyone give me a hint please? Thanks.