Question

If $\sqrt{- 1}$ = i &ω is a non real cube root of unity then the value of determinant is- $\left| \begin{matrix} x + 1 & \omega & \omega^{2} \\ \omega & x + \omega^{2} & 1 \\ \omega^{2} & 1 & x + \omega \end{matrix} \right|$

• A. x³
• B. x³ – 1
• C. x³ + 1
• D. None of these

Answer 1

Answer: (A)

x³

Answer 2

(x + 1 + ω + ω²) $\left| \begin{matrix} 1 & 1 & 1 \\ \omega & x + \omega^{2} & 1 \\ \omega^{2} & 1 & x + \omega \end{matrix} \right|$

= x[{x² – (ω – ω²)²} – (1 – ω)(1 – ω²)]

= x³