Linear Algebra proof

  • Thread starter Fosheimdet
  • Start date
  • #1
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2

Homework Statement



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.

Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
lurflurf
Homework Helper
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Hint what is

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

what is

$$(I-A)\sum_{j=0}^m \, A^j$$
 

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