If $\alpha$ is a root of the equation $x^2-x+1=0$ then $\left(\alpha+\frac{1}{\alpha}\right)^3+\left(\alpha^2+\frac{1}{\alpha^2}\right)^3+\left(\alpha^3+\frac{1}{\alpha^3}\right)^3+\left(\alpha^4+\frac{1}{\alpha^4}\right)^3+\ldots$ to 12 terms $=$

• A

  $-32$
• B

  $32$
• Correct answer
  C

  $0$
• D

  $16$

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