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Recall that two n xn matrices A and B are similar if there is an invertible matrix P such that P-'AP = B. Based on this definition of similarity, (a) show that if A and B are similar, then det A = det B. (Hint: Recall properties of determinants). (b) show that if A and B are similar, then A? and B² are also similar.

Recall that two n xn matrices A and B are similar if there is an invertible matrix P such that P-'AP = B. Based on this definition of similarity, (a) show that if A and B are similar, then det A = det B. (Hint: Recall properties of determinants). (b) show that if A and B are similar, then A? and B² are also similar.

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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Recall that two n x n matrices A and B are similar if there is an invertible matrix P such that P-AP = B. Based on this definition of similarity, (a) show that if A and B are similar, then det A = det B . (Hint: Recall properties of determinants). (b) show that if A and B are similar, then A? and B2 are also similar.
Transcribed Image Text:Recall that two n x n matrices A and B are similar if there is an invertible matrix P such that P-AP = B. Based on this definition of similarity, (a) show that if A and B are similar, then det A = det B . (Hint: Recall properties of determinants). (b) show that if A and B are similar, then A? and B2 are also similar.
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