Prove or give a counterexample: If A and B have the same characteristic polynomial, then

Chapter 6, Problem 8

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QUESTION:

Prove or give a counterexample: If A and B have the same characteristic polynomial, then A and B are similar.

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QUESTION:

Prove or give a counterexample: If A and B have the same characteristic polynomial, then A and B are similar.

ANSWER:

Step 1 of 2

Consider A and B as the two matrices of order n where A is non -singular matrix. Then,

                                                                     

The above expression suggest that AB and BA are similar. Thus, both have same characteristics polynomial, eigenvalues and multiplicities.

 

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