Hello,

I'm a bit bloqued on a little demontration.

A^4=0 , (I-A)^-1 = I²+A+A²+A³

Here is what i've done:

I=(I-A).(I²+AI+A²I+A³I)

=> I=I³+AI²+A²I²+A³I³-AI²-A²I-A³I-(A^4)I

=> I=I+A²+A³-A²-A³-A^4

=> I=I-A^4

=> A^4=0

But it is prove in reverse...

The right way:

If you know that matrix A^4=0, how to prove that (I-A)^-1 = I²+A+A²+A³

But in ths case (harder I supose), I don't know how to do.

Can you help me?