Linear Algebra

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Which One is Nilpotent?

LINALG-E4JGMC

Which of the following matrices is nilpotent?

A

$\begin{pmatrix}-1&0\\\ 0&1\end{pmatrix}$

B

$\begin{pmatrix}2&0\\\ 0&1\end{pmatrix}$

C

$\begin{pmatrix}1&2\\\ 3&4\end{pmatrix}$

D

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

E

$\begin{pmatrix}5&-3&2\\\ 15&-9&6\\\ 10&-6&4\end{pmatrix}$