[QUE/VS-10008]

In \(C^3\) with scalar product \((x,y)=x^\dagger y\) find the adjoint of operator \(A\) where \(A\) is defined to be
\begin{equation}
    A  \begin{pmatrix}x_1\\ x_2\\ x_3 \end{pmatrix}
     = \begin{pmatrix}x_1+ i x_3\\ x_2+i x_1 - ix_3 \\ x_1-i x_3\end{pmatrix}
\end{equation}