If \( A=\left[\begin{array}{rr}\cos x & \sin x \\ -\sin x & \cos x\...

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If \( A=\left[\begin{array}{rr}\cos x & \sin x \\ -\sin x & \cos x\end{array}\right] \) and \( A(\operatorname{adj} A)=\left[\begin{array}{ll}k & 0 \\ 0 & k\end{array}\right] \), then \( k= \)
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