Find the adjoint of the given matrix and verify in each case that \...

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Find the adjoint of the given matrix and verify in each case that \( A \cdot(\operatorname{adj} A)=(\operatorname{adj} A) \cdot A=|A| \cdot I \).
\( \mathrm{P} \)
\[
-\left[\begin{array}{ccc}
\cos \alpha & -\sin \alpha & 0 \\
\sin \alpha & \cos \alpha & 0 \\
0 & 0 & 1
\end{array}\right]
\]
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