Geometrical Matrix

Geometry Level 3

[cos(2π7)sin(2π7)sin(2π7)cos(2π7)]k=[1001]\begin{bmatrix}{\cos\left(\frac{2\pi}7\right)} & {-\sin\left(\frac{2\pi}7\right)} \\ {\sin\left(\frac{2\pi}7\right)} & {\cos\left(\frac{2\pi}7\right)}\end{bmatrix} ^k = \begin{bmatrix}{1} &{0} \\ {0} & {1}\end{bmatrix}

Find the least positive integral value of kk which satisfy the matrix equation above.

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