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## 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.

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- Thread starter Fosheimdet
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- #1

- 15

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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

lurflurf

Homework Helper

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Hint what is

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

what is

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

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

what is

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

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