Which of the following is a nilpotent matrix - Vidyadip

MCQ

Which of the following is a nilpotent matrix

A
$\left[ {\begin{array}{*{20}{c}}1&0\\0&1\end{array}} \right]$
B
$\left[ {\begin{array}{*{20}{c}}{\cos \theta }&{ - \sin \theta }\\{\sin \theta }&{\cos \theta }\end{array}} \right]$
✓
$\left[ {\begin{array}{*{20}{c}}0&0\\1&0\end{array}} \right]$
D
$\left[ {\begin{array}{*{20}{c}}1&1\\1&1\end{array}} \right]$

✓

Answer

Correct option: C.

$\left[ {\begin{array}{*{20}{c}}0&0\\1&0\end{array}} \right]$

c
$A$ is nilpotent if $A^m = 0$ and $A^{m-1} \neq 0$

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