If A is an n x n matrix, then A is called nilpotent if Ak = O

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If A is an n x n matrix, then A is called nilpotent if Ak = O for some positive integer k.
(a) Prove that every nilpotent matrix is singular.
(b) Verify that

is nilpotent.
(c) If A is nilpotent, prove that In - A is nonsingular.

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Elementary Linear Algebra with Applications

ISBN: 978-0132296540

9th edition

Authors: Bernard Kolman, David Hill

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Question Posted: Jun 21, 2016 06:58 AM

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If A is an n x n matrix, then A is called nilpotent if Ak = O

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a If A were nonsingular then products of A with itself must also be ...View the full answer

Elementary Linear Algebra with Applications

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