Show that the matrices

$\displaystyle A=\begin{bmatrix}1&3&0\\0&2&4\\0&0&3\end{bmatrix} \ \text{and} \ \begin{bmatrix}1&0&0\\0&2&5\\0&0&3\end{bmatrix}$

are similar and satisfy $\displaystyle \sum_{i,j}|a_{i,j}|^2=\sum_{i,j}|b_{i,j}|^2$ but are not unitary equivalent.

I am find it had to find a matrix S such that B=SAS^{-1}.