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MCQ

$\left| {\,\begin{array}{*{20}{c}}1&1&1\\1&{{\omega ^2}}&\omega \\1&\omega &{{\omega ^2}}\end{array}\,} \right| = $

✓
$3\sqrt 3 i$
B
$ - 3\sqrt 3 i$
C
$i\sqrt 3 $
D
$3$

✓

Answer

Correct option: A.

$3\sqrt 3 i$

a
(a) $\left| {\,\begin{array}{*{20}{c}}1&1&1\\1&{{\omega ^2}}&\omega \\1&\omega &{{\omega ^2}}\end{array}\,} \right|\, = 3(\omega - {\omega ^2})$

$ = 3\,\left[ {\frac{{ - 1 + \sqrt 3 i}}{2} - \frac{{ - 1 - \sqrt 3 i}}{2}} \right] = 3\sqrt 3 \,i$.

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