[QUE/VS-10006]

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+ x_2\\ x_2+x_3 \\ x_3+x_1\end{pmatrix}
\end{equation}