Answer each of the following questions in one word or one sentence ...

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Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
If \( A=\left[\begin{array}{rr}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right] \) and \( A(\operatorname{adj} A)=\left[\begin{array}{ll}k & 0 \\ 0 & k\end{array}\right] \), then find the value of \( k \).
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