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Linear Algebra proof

  1. Sep 15, 2013 #1
    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
  2. jcsd
  3. Sep 15, 2013 #2


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    Homework Helper

    Hint what is

    $$\sum_{j=0}^m \, A^j$$

    what is

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