A question in simillarity of matrices I have a 4x4 matrix 
$$ A = 
\left[ 
\begin{matrix}
0 & 1 & 0 & 0 \\
0 & 0 & 1 & 0 \\
1 & 0 & 0 & 0 \\
0 & 1 & 1 & 1
\end{matrix}
\right] $$
and i want to check if there is any similar matrix of matrix $A$ of the form:
$$ B = 
\left[ 
\begin{matrix}
0 & 0 & x & y \\
0 & 0 & z & w \\
a & b & 0 & 0 \\
c & d & 0 & 0
\end{matrix}
\right] $$
Is there any way to come in a conclusion if there such of this form similarity ? 
thanks.

note that two similar matrix have the same caracteristic polinomial $P(t)$, if we calcul this polynomial for each matrix we tack an have coefficient -1 at $t^3$ and othere $0$ as coefficient at $t^3$ so  the similarity is impossible
