Question

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

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

Answer 1

Answer: (B)

$\omega$

$\Delta ={\omega }^2-2{\omega }^2=-{\omega }^2$
${\Delta }^2={\omega }^4=\omega$
Ans: B