Linear algebra: inverse of the sum of two matrices

[degs2k4]

Homework Statement

Show that $$(I-A)^{-1} = I + A + A^2 + A^3$$ if $$A^4=0$$

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.

 

[Dick]

Just multiply (I-A) by I+A+A^2+A^3 and see if you get I.

 

[degs2k4]

Just multiply (I-A) by I+A+A^2+A^3 and see if you get I.

Thanks for your reply, got it solved!