The matrix A = begin{bmatrix} 1 & -3 & -4 -1 | vedclass

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(A) To find the index of nilpotency,we calculate $A^2$:$A^2 = \begin{bmatrix} 1 & -3 & -4 \ -1 & 3 & 4 \ 1 & -3 & -4 \end{bmatrix} \begin{bmatrix} 1

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$2$

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(A) To find the index of nilpotency,we calculate $A^2$:$A^2 = \begin{bmatrix} 1 & -3 & -4 \ -1 & 3 & 4 \ 1 & -3 & -4 \end{bmatrix} \begin{bmatrix} 1 & -3 & -4 \ -1 & 3 & 4 \ 1 & -3 & -4 \end{bmatrix}$$A^2 = \begin{bmatrix} (1-1-4) & (-3+9+12) & (-4-12+16) \ (-1+3+4) & (3-9-12) & (4+12-16) \ (1+3-4) & (-3-9+12) & (-4-12+16) \end{bmatrix} = \begin{bmatrix} 0 & 0 & 0 \ 0 & 0 & 0 \ 0 & 0 & 0 \end{bmatrix} = O$Since $A^2 = O$ and $A 
eq O$,the matrix $A$ is nilpotent of index $2$.

The matrix $A = \begin{bmatrix} 1 & -3 & -4 \\ -1 & 3 & 4 \\ 1 & -3 & -4 \end{bmatrix}$ is nilpotent of index:

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