A problem on matrices: Find the value of $k$ 
If $
        \begin{bmatrix}
        \cos \frac{2 \pi}{7} & -\sin \frac{2 \pi}{7} \\
        \sin \frac{2 \pi}{7} & \cos \frac{2 \pi}{7}  \\
        \end{bmatrix}^k
 = 
        \begin{bmatrix}
        1 & 0 \\
        0 & 1 \\
        \end{bmatrix}
$, then the least positive integral value of $k$ is?

Actually, I got no idea how to solve this.
 I did trial and error method and got 7 as the answer.
how do i solve this? Can you please offer your assistance? Thank you

I founded out that $$A^k=
        \begin{bmatrix}
        \cos \frac{k.2 \pi}{7} & -\sin \frac{k.2 \pi}{7} \\
        \sin \frac{k.2 \pi}{7} & \cos \frac{k.2 \pi}{7}  \\
        \end{bmatrix}
$$
using appropriate trigonometric formulae. Now for $A=I$, $k$ should be equal to $7$ 
