1. Sep 15, 2013 #1

   Fosheimdet

   

   1. The problem statement, all variables and given/known data
   
   Let A be a nxn matrix, and I the corresponding identity matrix, both in the real numbers ℝ. Assume that A^m=0 for a positive integer m. Show that I-A is an invertible matrix.
   
   2. Relevant equations
   
   
   
   3. The attempt at a solution

    

   Fosheimdet, Sep 15, 2013
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3. Sep 15, 2013 #2

   lurflurf

   

   Homework Helper

   Hint what is
   
   $$\sum_{j=0}^m \, A^j$$
   
   what is
   
   $$(I-A)\sum_{j=0}^m \, A^j$$

    

   lurflurf, Sep 15, 2013

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