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If \( \left(\begin{array}{cc}1 & -\tan \theta \\ \tan \theta & 1\end{array}\right)\left(\begin{array}{cc}1 & \tan \theta \\ -\tan \theta & 1\end{array}\right)^{-1}=\left[\begin{array}{cc}a & -b \\ b & a\end{array}\right] \), then
(A) \( a=\sin 2 \theta, b=\cos 2 \theta \)
(B) \( a=b=1 \)
(C) \( a=1, b=\sin 2 \theta \)
(D) \( a=\cos 2 \theta, b=\sin 2 \theta \)
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