Question

If ω be a complex cube root of unity, then

$\left| \begin{matrix} 1 & \omega & - \omega^{2}/2 \\ 1 & 1 & 1 \\ 1 & - 1 & 0 \end{matrix} \right|$is equal to

• A. 0
• B. 1
• C. ω
• D. ω²

Answer 1

Answer: (A)

0

Answer 2

$\left| \begin{matrix} 1 & \omega & - \omega^{2}/2 \\ 1 & 1 & 1 \\ 1 & - 1 & 0 \end{matrix} \right|$= –$\frac{1}{2}\left| \begin{matrix} 1 & \omega & \omega^{2} \\ 1 & 1 & - 2 \\ 1 & - 1 & 0 \end{matrix} \right|$

=$\frac{1}{2}\left| \begin{matrix} 1 + \omega + \omega^{2} & \omega & \omega^{2} \\ 0 & 1 & - 2 \\ 0 & - 1 & 0 \end{matrix} \right|$ = –$\frac{1}{2}\left| \begin{matrix} 0 & \omega & \omega^{2} \\ 0 & 1 & - 2 \\ 0 & - 1 & 0 \end{matrix} \right|$= 0