# Explicit expression for inverse of I-A

1. Nov 19, 2012

### peripatein

Hello,
This is not a homework exercise, so I decided to post it here. Hopefully one of you could help.
I would like to find an explicit expression for (I-A)^(-1), provided that A is a squared matrix (nxn) and A^k = 0. It is also given that I-A^k = (I-A)(I+A+A^2+...+A^(k-1)).
I understand that by definition the inverse matrix of I-A will be (I+A+A^2+...+A^(k-1)), but is there a way to arrive at a more simplified, explicit expression (yet without knowing what A is)?

2. Nov 19, 2012

### micromass

I don't understand why

$$I+A+A^2+...+A^{k-1}$$

isn't good enough for you. It's an explicit expression.

To my knowledge, there is no other expression.