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STD 12 - 3 and 4 . determinant and metrices — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 3 and 4 . determinant and metrices1 Mark
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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