Finding the order of an element in the dihedral group of order 4. How do I find the order of 
$$S_1=\left({\begin{array}{cc}
   \cos\frac{\pi}{3} & \sin\frac{\pi}{3}\\
   \sin\frac{\pi}{3} & -\cos\frac{\pi}{3}\\
  \end{array} }\right)$$
I know that $S_1$ is a dihedral group and is a reflection of the line that makes an angle of $\frac{\pi}{3}$ with the x-axis.. but finding its order is what I don't know how to do.. Please help.

$$S_1^2=\begin{bmatrix} 1&0\\0&1\end{bmatrix}$$
In more detail
$$\begin{align}S_1^2=&\begin{matrix} \cos^2{\frac{\pi}{3}}+\sin^2{\frac{\pi}{3}}&\cos{\frac{\pi}{3}}\sin{\frac{\pi}{3}}-\cos{\frac{\pi}{3}}\sin{\frac{\pi}{3}}\\\cos{\frac{\pi}{3}}\sin{\frac{\pi}{3}}-\cos{\frac{\pi}{3}}\sin{\frac{\pi}{3}}&\cos^2{\frac{\pi}{3}}+\sin^2{\frac{\pi}{3}}\end{matrix}\end{align}$$
And so the order is $2$. By the way reflection is always of order two
