The matrix A = [ * 20 c 1& - 3 & - 4 - 1 & , , ,3 & , ,4 1& - 3 &… - Vidyadip

MCQ

The matrix $A = \left[ {\begin{array}{*{20}{c}}1&{ - 3}&{ - 4}\\{ - 1}&{\,\,\,3}&{\,\,4}\\1&{ - 3}&{ - 4}\end{array}} \right]$ is nilpotent of index

✓
$2$
B
$3$
C
$4$
D
$6$

✓

Answer

Correct option: A.

$2$

a
(a) Since ${A^2} = O$ (Zero matrix) and $2$ is the least $+ve $ integer for which

${A^2} = O$. Thus, $A$ is nilpotent of index $2$.

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