Is this a family of similar matrices $\left(\begin{smallmatrix} 0&x\\ 0&0 \end{smallmatrix}\right)$? Is matrix $A = \begin{pmatrix} 0&1\\ 0&0 \end{pmatrix}$ similar to matrix $B=\begin{pmatrix} 0&2\\ 0&0 \end{pmatrix}$? If so, how do I prove this?
I came here from following the answer to this question:
Do similar matrices have equal singular values?

If they are similar then  
$\begin{pmatrix} a&b\\ c&d \end{pmatrix}  \begin{pmatrix} 0&1\\ 0&0 \end{pmatrix}=  \begin{pmatrix} 0&2\\ 0&0 \end{pmatrix}  \begin{pmatrix} a&b\\ c&d \end{pmatrix} $ 
for some invertible matrix $P=\begin{pmatrix} a&b\\ c&d \end{pmatrix}$. 
Try to calculate such matrix $P$ from the above condition.
