Which of following is a nilpotent matrix

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3 and 4 .Determinants and Matrices

easy

Which of the following is a nilpotent matrix

A

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

B

$\left[ {\begin{array}{*{20}{c}}{\cos \theta }&{ - \sin \theta }\\{\sin \theta }&{\cos \theta }\end{array}} \right]$

C

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

D

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

Solution

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

Standard 12

Mathematics

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