A = $\begin{bmatrix} 3i & -1+i & 3-2i \\[0.3em] 1+i &- i & 1+2i \\[0.3em] -3-2i & -1+2i &0 \end{bmatrix}$

Hence $\bar A $ of A is

$\bar A=$$\begin{bmatrix} -3i & -1-i & 3+2i \[0.3em] 1-i & i & 1-2i \[0.3em] -3+2i & -1-2i &0 \end{bmatrix}$ ---   $P =\dfrac 12(A + \bar A)$ $=\dfrac 1 2$$\begin{bmatrix} 0& -2 & 6 \[0.3em] 2 & 0 & 2\[0.3em] -6 & -2 &0 \end{bmatrix}$ ---   $P = \begin{bmatrix} 0& -1 & 3 \[0.3em] 1 & 0 & 1\[0.3em] -3 & -1 &0 \end{bmatrix}$   $Q = \dfrac {1}{2i}(A - \bar A)$ $=\dfrac {1}{ 2i}$$\begin{bmatrix} 6i & 2i & -4i \[0.3em] 2i & -2i & 4i \[0.3em] -4i & 4i &0 \end{bmatrix}$   $Q = \begin{bmatrix} 3& 1 & -2 \[0.3em] 1 & -1 &2\[0.3em] -2 &2 &0 \end{bmatrix}$ --- $A = P + iQ$ = $\begin{bmatrix} 0& -1 & 3 \[0.3em] 1 & 0 & 1\[0.3em] -3 & -1 &0 \end{bmatrix}$+ i $\begin{bmatrix} 3& 1 & -2 \[0.3em] 1 & -1 &2\[0.3em] -2 &2 &0 \end{bmatrix}$