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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
If $X$  is a square matrix of order  $ 3 × 3$  and $\lambda $ is a scalar, then adj ($\lambda X)$ is equal to
  • A
    $\lambda \,adjX$
  • B
    ${\lambda ^3}adj\,X$
  • ✓
    ${\lambda ^2}adj\,X$
  • D
    ${\lambda ^4}adj\,X$
✓

Answer

Correct option: C.
${\lambda ^2}adj\,X$
c
(c) By fundamental property, $adj(\lambda X) = {\lambda ^{n - 1}}(adj\,X)$.

Here $n = 3$

$\therefore$ $adj(\lambda X) = {\lambda ^{3 - 1}}(adj\,X)$

$adj(\lambda X) = {\lambda ^2}(adj\,X)$.

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