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$A=\left[\begin{array}{ccc}1 & -3 & -4 \\ -1 & 3 & 4 \\ 1 & -3 & -4\end{array}\right]$ is nilpotent of index
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$2$
Since $A^2=O$ (Zero matrix) and 2 is the least +ve integer for which $A^2=0$. Thus, $A$ is nilpotent of index 2 .
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