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The matrix $A = [\begin{array}{rrr} 1 - 3 - 4 \\ - 1 3 4 \\ 1 - 3 - 4 \end{array}]$ is nilpotent
index

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Correct option is A

We know that a square matrix A is nilpotent index n, if n is the least positive integer such that An=O O(null matrix)For the given matrix, we have An=OHence, it is a nilpotent matrix of index 2

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The matrix A=1 −3 −4−1 3 41 −3 −4 is nilpotent index

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The matrix $A = [\begin{array}{rrr} 1 - 3 - 4 \\ - 1 3 4 \\ 1 - 3 - 4 \end{array}]$ is nilpotent
index