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Linear algebra: inverse of the sum of two matrices

  1. Aug 10, 2010 #1
    1. The problem statement, all variables and given/known data

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

    3. 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.
  2. jcsd
  3. Aug 10, 2010 #2


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    Just multiply (I-A) by I+A+A^2+A^3 and see if you get I.
  4. Aug 10, 2010 #3
    Thanks for your reply, got it solved!
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