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## Homework Statement

Show that [tex] (I-A)^{-1} = I + A + A^2 + A^3 [/tex] if [tex]A^4=0[/tex]

## The Attempt at a Solution

I found at Google Books some kind of formula for it:

http://books.google.com/books?id=UQ...PA44#v=onepage&q=inverse sum matrices&f=false

However, I think I should develop some kind of series for it using I = A(A^-1), I tried but I haven't been successful...

Thanks in advance.