Linear algebra: inverse of the sum of two matrices

  • Thread starter degs2k4
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  • #1
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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.
 

Answers and Replies

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

Thanks for your reply, got it solved!
 

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