If ω is a cube root of unity and Δ = ∣ ∣ ∣ 1 2 ω ω ω 2 ∣ ∣ ∣ , then Δ 2 is equal to Options: A . &nbsp−ω B . &nbspω2 C . &nbsp1 D . &nbspω

If ω is a cube root of unity and Δ = ∣∣"

Question

ω

is a cube root of unity and

Δ = ∣ ∣ ∣ \begin{matrix} 1 & 2 ω ω & ω^{2} \end{matrix} ∣ ∣ ∣

, then

Δ^{2}

is equal to

Options:

A . −ω

B . ω2

C . 1

D . ω

Answer: Option D
:
D
Since

Δ = ω^{2} - 2 ω^{2} = - ω^{2} .

Therefore

Δ^{2} = ω^{4} = ω .

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