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Let A be an n×n matrix. If there exists k > n such that A^k =0,then...

Let A be an n×n matrix. If there exists k > n such that A^k =0,then
(a) prove that In − A is nonsingular, where In is the n × n identity matrix;
(b) show that there exists r ≤ n such that A^r= 0.

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