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Consider the statements below. Verify which statements are true and which ones are false. Justify your answer briefly in case you claim a statement is false. i. If A and B are two invertible matrices of the same order then AB = BA. ii. ABC + ADC = A(D+B)C. iii. det(AA) = \det(A) for all A Є R. iv. tr(AB) = tr(BA). v. ((AB)-¹)T = (B-¹)T(A-¹)T.

Consider the statements below. Verify which statements are true and which ones are false. Justify your answer briefly in case you claim a statement is false. i. If A and B are two invertible matrices of the same order then AB = BA. ii. ABC + ADC = A(D+B)C. iii. det(AA) = \det(A) for all A Є R. iv. tr(AB) = tr(BA). v. ((AB)-¹)T = (B-¹)T(A-¹)T.

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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Consider the statements below. Verify which statements are true and which ones are false. Justify your answer briefly in case you claim a statement is false. i. If A and B are two invertible matrices of the same order then AB = BA. ii. ABC + ADC = A(D+B)C. iii. det(AA) = \det(A) for all A Є R. iv. tr(AB) = tr(BA). v. ((AB)-¹)T = (B-¹)T(A-¹)T.
Transcribed Image Text:Consider the statements below. Verify which statements are true and which ones are false. Justify your answer briefly in case you claim a statement is false. i. If A and B are two invertible matrices of the same order then AB = BA. ii. ABC + ADC = A(D+B)C. iii. det(AA) = \det(A) for all A Є R. iv. tr(AB) = tr(BA). v. ((AB)-¹)T = (B-¹)T(A-¹)T.
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