Is there an example such that $A$ and $B$, three by three, that have the same eigenvectors, but different eigenvalues?
What would be the eigenvectors and eigenvalues if it exists because I'm stuck on this practice problem.
I know that if matrices $A$ and $B$ can be written such that $AB=BA$, they share the same eigenvectors, but what about their eigenvalues? precisely if they're squared matrices ($3\times 3$ case)
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