Question

If $\omega$ is a cube root of unity and$\Delta = \left| \begin{matrix} 1 & 2\omega \\ \omega & \omega^{2} \end{matrix} \right|$, then $\Delta^{2}$is equal to.

• A. $- \omega$
• B. $\omega$
• C. 1
• D. $\omega^{2}$

Answer 1

Answer: (B)

$\omega$

Answer 2

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