Nilpotent endomorphism/4x4/Possibilities/Exercise

Show that every nilpotent endomorphism, on a four-dimensional space, can be brought into exactly one of the following forms.

${\begin{pmatrix}0&0&0&0\\0&0&0&0\\0&0&0&0\\0&0&0&0\end{pmatrix}},\,{\begin{pmatrix}0&0&0&0\\0&0&0&0\\0&0&0&1\\0&0&0&0\end{pmatrix}},\,{\begin{pmatrix}0&1&0&0\\0&0&0&0\\0&0&0&1\\0&0&0&0\end{pmatrix}},\,{\begin{pmatrix}0&0&0&0\\0&0&1&0\\0&0&0&1\\0&0&0&0\end{pmatrix}},\,{\begin{pmatrix}0&1&0&0\\0&0&1&0\\0&0&0&1\\0&0&0&0\end{pmatrix}}.$

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