If $\left[ \begin{array}{l}\cos \theta \,\,\,\, - \sin \theta \,\,\,\,\,\,0\\\sin \theta \,\,\,\,\,\,\,\,\cos \theta \,\,\,\,\,\,0\\0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0\,\,\,\,\,\,\,\,\,\,\,1\end{array} \right]$, then $adjA =$

$A=\begin{bmatrix} cos\theta & -\sin\theta & 0 \\ \sin\theta & \cos\theta & 0 \\ 0 & 0 & 1 \end{bmatrix}$

lets write co factor

$C_{11}=\cos\theta$ $C_{12}=-\sin\theta$ $C_{13}=0$

$C_{21}=\sin\theta$ $C_{22}=\cos\theta$ $C_{23}=0$

$C_{31}=0$ $C_{32}=0$ $C_{33}=1$

$\therefore$ co factor matrix

$=\begin{bmatrix} \cos\theta & -\sin\theta & 0 \\ \sin\theta & \cos\theta & 0 \\ 0 & 0 & 1 \end{bmatrix}$

$\therefore Adj\,A=$ transpose of cofactor matrix

$=\begin{bmatrix} \cos\theta & -\sin\theta & 0 \\ \sin\theta & \cos\theta & 0 \\ 0 & 0 & 1 \end{bmatrix}$

$=A^T$