If \(A = \left[ {\begin{array}{*{20}{c}}
{\cos \,\theta }&{ - \sin \,\theta }\\
{\sin \,\theta }&{\cos \,\theta }
\end{array}} \right]\), then the matrix \({A^{ - 50}}\) when \(\theta  = \frac{\pi }{{12}}\) is equal to 

1. A \(\left[ {\begin{array}{*{20}{c}}
   {\frac{1}{2}}&{ - \frac{{\sqrt 3 }}{2}}\\
   {\frac{{\sqrt 3 }}{2}}&{\frac{1}{2}}
   \end{array}} \right]\)
2. B \(\left[ {\begin{array}{*{20}{c}}
   {\frac{{\sqrt 3 }}{2}}&{ - \frac{1}{2}}\\
   {\frac{1}{2}}&{\frac{{\sqrt 3 }}{2}}
   \end{array}} \right]\)
3. C \(\left[ {\begin{array}{*{20}{c}}
   {\frac{{\sqrt 3 }}{2}}&{\frac{1}{2}}\\
   { - \frac{1}{2}}&{\frac{{\sqrt 3 }}{2}}
   \end{array}} \right]\)
4. D \(\left[ {\begin{array}{*{20}{c}}
   {\frac{1}{2}}&{\frac{{\sqrt 3 }}{2}}\\
   { - \frac{{\sqrt 3 }}{2}}&{\frac{1}{2}}
   \end{array}} \right]\)