If A is satisfied as A2 - 6A + 5In = 0, what is A-1 If an n x n matrix A satisfies A? – 6A + 5I, = 0, then A-1O is (1/5)(61, - ).O is (1/5)(A – 6Im).O does not exist.O may exist only if n > 6.O exists, but there is not enough information to determine it.exists only ifn < 6.

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If an n × n matrix A satisfies A? – 6A + 5In = 0, then O is (1/5)(6In – A). O is (1/5)(A – 6In). O does not exist.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.5: Subspaces, Basis, Dimension, And Rank

Problem 63EQ

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If A is satisfied as A² - 6A + 5I_n = 0, what is A^-1

If an n x n matrix A satisfies A? – 6A + 5I, = 0, then A-1
O is (1/5)(61, - ).
O is (1/5)(A – 6Im).
O does not exist.
O may exist only if n > 6.
O exists, but there is not enough information to determine it.
exists only ifn < 6.

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