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Prove that AB has the same eigenvalues as BA

Chapter 5, Problem 5.6.42

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QUESTION:

Prove that AB has the same eigenvalues as BA.

Questions & Answers

QUESTION:

Prove that AB has the same eigenvalues as BA.

ANSWER:

Step 1 of 3

If  and  are  matrices, then for a scalar 

 is an eigen value of  ,then there is  such that  

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