Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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14. Which statements are true, and which are false? If the statement is false, provide a specific counterexample, and
show why it works. If the statement is true, explain why.
(a) AB = BA for any n x n matrices A, B.
(b) Let A, B be n x n matrices. If AB = BA, then (A + B)(A − B) = A² - B².
(c) Let A, B be 2 x 2 matrices. If A² = AB and det(A) = 4, then A = B.
(d) Let A, B be two n x n matrices. If AB = 0, then A = 0 or B = 0.
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Transcribed Image Text:14. Which statements are true, and which are false? If the statement is false, provide a specific counterexample, and show why it works. If the statement is true, explain why. (a) AB = BA for any n x n matrices A, B. (b) Let A, B be n x n matrices. If AB = BA, then (A + B)(A − B) = A² - B². (c) Let A, B be 2 x 2 matrices. If A² = AB and det(A) = 4, then A = B. (d) Let A, B be two n x n matrices. If AB = 0, then A = 0 or B = 0.
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