If
\[
A=
\begin{bmatrix}
\frac12 & \frac{\sqrt3}{2}\\
-\frac{\sqrt3}{2} & \frac12
\end{bmatrix},
\]
then $A^{10}=$}
Show Hint
Whenever a matrix contains $\cos\theta$ and $\sin\theta$ in rotation form, use
\[
R(\theta)^n=R(n\theta).
\]
This avoids lengthy matrix multiplication.