Homework Help: Linear algebra: inverse of the sum of two matrices

1. Aug 10, 2010

degs2k4

1. The problem statement, all variables and given/known data

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

3. 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...

2. Aug 10, 2010

Dick

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

3. Aug 10, 2010