If \( \alpha, \beta \) are nonreal numbers satisfying \( x^{3}-1=0 \) then the value of \( \left...
If \( \alpha, \beta \) are nonreal numbers satisfying \( x^{3}-1=0 \) then the value of \( \left|\begin{array}{ccc}\lambda+1 & \alpha & \beta \\ \alpha & \lambda+\beta & 1 \\ \beta & 1 & \lambda+\alpha\end{array}\right| \) is equal to
(a) 0
(b) \( \lambda^{3} \)
(c) \( \lambda^{3}+1 \)
(d) none of these
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