Question

If $\sqrt{- 1}$ = $a = 2 , b = 4$ and $\left[ \begin{array} { l l l } x & y & z \end{array} \right] \left[ \begin{array} { l l l } a & h & g \\ h & b & f \\ g & f & c \end{array} \right] \left[ \begin{array} { l } x \\ y \\ z \end{array} \right]$ is a non real cube root of unity then the

value of $\left| \begin{matrix} 1 & \omega^{2} & 1 + i + \omega^{2} \\ –i & - 1 & - 1 - i + \omega \\ 1 - i & \omega^{2} - 1 & - 1 \end{matrix} \right|$is equal to :

• A. 1
• B. $i$
• C. $\omega$
• D. 0

Answer 1

Answer: (D)

0

Answer 2

R₁ → R₁ + R₂ – R₃

= $\left| \begin{matrix} 0 & 0 & 1 + \omega + \omega^{2} \

• i & - 1 & - 1 - i + \omega \ 1 - i & \omega^{2} - 1 & - 1 \end{matrix} \right|$

= $\left| \begin{matrix} 0 & 0 & 0 \

• i & - 1 & - 1 - i + \omega \ 1 - i & \omega^{2} - 1 & - 1 \end{matrix} \right|$ = 0