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**Alterah** I have a question regarding two matrices. Are the following matrices similar and if so find a third matrix P such that:

$\displaystyle B = P^{-1}AP$

A = $\displaystyle \left(\begin{array}{ccc}1&0&0\\0&2&0\\0&0&3\end{ar ray}\right)$

B = $\displaystyle \left(\begin{array}{ccc}3&0&0\\0&2&0\\0&0&1\end{ar ray}\right)$

As far as I can tell they are similar because they have the same eigenvalues: 1, 2, 3. If I plug in 1 for

$\displaystyle \lambda I - A$

I get:

$\displaystyle \left(\begin{array}{ccc}0&0&0\\0&-1&0\\0&0&-2\end{array}\right)$

This row reduces to:

$\displaystyle \left(\begin{array}{ccc}0&1&0\\0&1&0\\0&0&0\end{ar ray}\right)$

Doesn't that have the zero solution? My understanding of this topic regarding diagonalization isn't the best. Thanks for any help...I realize I have two more eigenvalues to find eigenvectors for.