If $P=\left[\begin{array}{cc}\frac{\sqrt{3}}{2}& \frac{1}{2}\\ -\frac{1}{2}& \frac{\sqrt{3}}{2}\end{array}\right], A=\left[\begin{array}{cc}1& 1\\ 0& 1\end{array}\right]$ and $Q=PA{P}^T,$ then $P^T Q^{2015} P$ is :

• A

  $\left[\begin{array}{cc}0& 2015\\ 0& 0\end{array}\right]$
• B

  $\left[\begin{array}{cc}2015& 0\\ 1& 2015\end{array}\right]$
• Correct answer
  C

  $\left[\begin{array}{cc}1& 2015\\ 0& 1\end{array}\right]$
• D

  $\left[\begin{array}{cc}2015& 1\\ 0& 2015\end{array}\right]$

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