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9. Which of the following statements refutes the claim that GLR(3), the set of 3 x 3 invertible matrices over the real numbers, is a field? A. There exist elements A and B of GLR(3) such that AB #BA. B. There exist elements A and B of GLR(3) such that det(AB) = det(A)det(B). C. If A is an element of GLR(3), then there exists a matrix A-1 such that A-¹A = I. D. If A is an element of GLR(3), then there exists a matrix A such that det(A) # 1.

9. Which of the following statements refutes the claim that GLR(3), the set of 3 x 3 invertible matrices over the real numbers, is a field? A. There exist elements A and B of GLR(3) such that AB #BA. B. There exist elements A and B of GLR(3) such that det(AB) = det(A)det(B). C. If A is an element of GLR(3), then there exists a matrix A-1 such that A-¹A = I. D. If A is an element of GLR(3), then there exists a matrix A such that det(A) # 1.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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9. Which of the following statements refutes the claim that GLR(3), the set of 3 x 3 invertible matrices over the real numbers, is a field? A. There exist elements A and B of GLR(3) such that AB #BA. B. There exist elements A and B of GLR(3) such that det(AB) = det(A)det(B). C. If A is an element of GLR(3), then there exists a matrix A-1 such that A-¹A = I. D. If A is an element of GLR(3), then there exists a matrix A such that det(A) # 1.
Transcribed Image Text:9. Which of the following statements refutes the claim that GLR(3), the set of 3 x 3 invertible matrices over the real numbers, is a field? A. There exist elements A and B of GLR(3) such that AB #BA. B. There exist elements A and B of GLR(3) such that det(AB) = det(A)det(B). C. If A is an element of GLR(3), then there exists a matrix A-1 such that A-¹A = I. D. If A is an element of GLR(3), then there exists a matrix A such that det(A) # 1.
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