Question

If $\omega(\neq 1)$ is a cube root of unity, then $\begin{vmatrix}1 & 1+ i +\omega^{2} & \omega^{2} \\ 1-i & -1 & \omega^{2}-1 \\ - i & - i +\omega-1 & -1\end{vmatrix}$ equals

• A. 0
• B. 1
• C. i
• D. $\omega$

Answer 1

Answer: (C)

given $3 * x * 2^{-1}=1 \Rightarrow 3 * x=1 * 2$
$\Rightarrow 7\left(\frac{3 x}{3}\right)=7\left(\frac{1.2}{3}\right)$
$ \Rightarrow 3 x=2 \therefore x=2 / 3$