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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 $\omega $ is a cube root of unity and $\Delta = \left| {\begin{array}{*{20}{c}}1&{2\omega }\\\omega &{{\omega ^2}}\end{array}} \right|$, then ${\Delta ^2}$ is equal to
  • A
    $ - \omega $
  • ✓
    $\omega $
  • C
    $1$
  • D
    ${\omega ^2}$
✓

Answer

Correct option: B.
$\omega $
b
(b) Since $\Delta = {\omega ^2} - 2{\omega ^2} = - {\omega ^2}$.

Therefore ${\Delta ^2} = {\omega ^4} = \omega $.

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