Consider this solution of the equation X 2 I 3 in the ring M 3 (R) X 2 I 3 implies X 2 I 3 0 the zero matrix, so factoring, we have (X I 3 )(X I 3 ) 0 Whence either X I 3 or X I 3 Is this reasoning correct If not, point out the error, and if possible, give a counterexample to the conclusion ...

This reasoning is not correct The statement X2 I3 0 does not imply that X I3X I3 0 To see ...

Consider this solution of the equation X 2 = I 3 in the ring M 3 (R).

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Consider this solution of the equation X² = I₃ in the ring M₃(R).

X² = I₃ implies X² -I₃ = 0. the zero matrix, so factoring, we have (X - I₃)(X + I₃) = 0

Whence either X = I₃ or X = -I₃

Is this reasoning correct? If not, point out the error, and if possible, give a counterexample to the conclusion.

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A First Course In Abstract Algebra

ISBN: 9780201763904

7th Edition

Authors: John Fraleigh

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Question Posted: Jan 04, 2023 05:05 AM

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Consider this solution of the equation X 2 = I 3 in the ring M 3 (R).

Question:

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This reasoning is not correct The statement X2 I3 0 does not imply that X I3X I3 0 To see ...View the full answer

A First Course In Abstract Algebra

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