Define a function such that $<X,Y> = \overline{Y^t}AX$ where $A$ is a real $3\times 3$ matrix and $X,Y$ are $3\times1$ complex matrices. Since,
$\overline{<X,Y>}=\overline{\overline{Y^t}AX}=Y^tA\overline{X}$
$Y^tA\overline{X}$ doesn't have to equal $<Y,X>=\overline{X^t}AY$ so this is not inner product. Is it a true way to show this?