# Linear algebra: inverse of the sum of two matrices

## 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:

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...

Dick