Given ${\bf A}$ is similar to a Jordan matrix find a nonsingular matrix $\bf P$ such that ${\bf P}^{-1}{\bf AP}={\bf J}$
$ {\bf A}= \begin{bmatrix} 0 & 0 & 0\\ 1 & 0 & 0\\ 0 & 1 & 1\\ \end{bmatrix} $
I have worked out $ {\bf J}= \begin{bmatrix} 0&0&0\\ 1&0&0\\ 0&0&1\\ \end{bmatrix} $
The textbook I am using shows an example where ${\bf A}$ has one eigenvalue. I am unsure how to apply this example to the question I have.
I am using "Matrices and Linear Transformations" by Cullen. The example I was looking at is on page204.
Please help.