If $\alpha=\cos \frac{\pi}{3}+i \sin \frac{\pi}{3}$ then the value of the determinant $\left|\begin{array}{ccc}1 & \alpha & \alpha^2 \\ \alpha^2 & 1 & \alpha \\ \alpha & \alpha^2 & 1\end{array}\right|$ is

• A

  0
• B

  1
• C

  -4
• Correct answer
  D

  4

Hence, the correct answer is option: 'D'.