I found the eigenvalues of both matrices. The characteristic equation for both matrices is $\displaystyle (\lambda+2)^2(-1-\lambda)$.Quote:

Are the following pairs of matrices similar:

$\displaystyle \begin{pmatrix}

{-2}&{1}&{0}\\

{0}&{-2}&{1}\\

{0}&{0}&{-1}

\end{pmatrix}$ and $\displaystyle \begin{pmatrix}

{-2}&{0}&{0}\\

{0}&{-2}&{0}\\

{0}&{-1}&{-1}

\end{pmatrix}$?

Hence the eigenvalues are -2 and -1 for both matrices.

Since the eigenvalues are the same for both matrices i'm pretty sure they're similar. However, the presence of a repeated eigenvalue (-2) makes me think they might not be.

Can anyone clarify this situation for me?