If is a cube root of unity and = | * 20 c 1& 2 & ^2 |, then ^2 is… - Vidyadip

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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