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?

Finding the eigenvalues of any of these matrices is not particularly difficult; they are all upper-triangular.
Hint: Suppose that $A$ is a $3 \times 3$ matrix with zero as its only (complex) eigenvalue.  Note that $A$ has the desired J-C form if and only if $A \neq 0$ but $A^2 = 0$ (why?).
