I have a question where I must prove that none of the following matrices are conjugate:(adsbygoogle = window.adsbygoogle || []).push({});

1 1 0

0 1 1

0 0 1

1 1 0

0 1 0

0 0 1

1 0 0

0 1 0

0 0 1

I started by working out the characteristic polynomials since if these were different, the matrices couldn't be conjugate. But all three have the same characteristic polynomial [(1-t)^3], so that didn't help me.

I'm not sure what else I can do from here. I know that if A and B are conjugate, A = QBP where Q is the inverse of the matrix P. Also, matrices are conjugate if they represent the same linear transformation after a change of basis.

But I'm not sure how to apply these definitions to a specific example.

Thanks in advance for any help.

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# Homework Help: Similar/conjugate matrices

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