<s>[INST] To find jordan canonical form Which of the following matrices have Jordan canonical form of equal to the $3\times 3$ matrix  
$$
\begin{pmatrix}
0 & 1 & 0 \\
0 & 0 & 0 \\
0 & 0 & 0
\end{pmatrix}$$
a)$
\begin{pmatrix}
0 & 0 & 1 \\
0 & 0 & 0 \\
0 & 0 & 0
\end{pmatrix}$
b)$
\begin{pmatrix}
0 & 0 & 1 \\
0 & 0 & 1 \\
0 & 0 & 0
\end{pmatrix}$
c)$
\begin{pmatrix}
0 & 1 & 1 \\
0 & 0 & 0 \\
0 & 0 & 0
\end{pmatrix}$
d)$
\begin{pmatrix}
0 & 1 & 1 \\
0 & 0 & 1 \\
0 & 0 & 0
\end{pmatrix}$
Here characteristic equation of the matrix is $x^3$.Hence the 3 eigenvalues of the matrix are zero.
Do we want to find the eigenvalues of all the matrices in the options?Is there any other way?
 [/INST] The given Jordan canonical form implies, minimal polynomial of corresponding matrix should be $x^2=0.$ Hence if matrix $A$ is having the property that $A \neq 0$ and $A^2=0 ,$ it will have desired Jordan canonical form.
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