If $A=\left[\begin{array}{ccc}\sin 2 \theta & 2 \sin ^2 \theta-1 & 0 \\ \cos 2 \theta & 2 \sin \theta \cos \theta & 0 \\ 0 & 0 & 1\end{array}\right]$, then which of the following statements is/are correct?

1. $A^{-1}=\operatorname{adj} A$

2. A is skew-symmetric matrix

3. $A^{-1}=A^T$

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