$4\times4$ matrices minimal polynomial Anyone can tell me how to find the minimal polynomial of $4\times4$ matrices belong to $M_4(\mathbb{R})$, because I know how to find $2\times2$ and $3\times3$ matrices, but never try to find $4\times4$. I think this should be linear algebra problem. Can anyone show me an example?  Or can use the example from my notebook.
$$A= \begin{pmatrix}
\phantom{-}3&-4&\phantom{-}0&\phantom{-}2\\
-4&-5&-2&\phantom{-}4\\
\phantom{-}0&\phantom{-}0&\phantom{-}3&-2\\
\phantom{-}0&\phantom{-}0&\phantom{-}2&-1
\end{pmatrix}$$
Thanks so much!

$A=\begin{pmatrix}
3&-4&0&2\\
-4&-5&-2&4\\
0&0&3&-2\\
0&0&2&-1\\
\end{pmatrix}$
Minimal polynomial of A will be the minimal polynomial of 
$X=\begin{pmatrix}
3&-4\\
-4&-5\\
\end{pmatrix}$ multiplied by the minimal polynomial of 
$Y=\begin{pmatrix}
3&-2\\
2&-1\\
\end{pmatrix}$
Reason:We have $A^k=\begin{pmatrix}
X^k&C_k\\
0&Y^k\\
\end{pmatrix}$
