How to show that in a 6 dimensional manifold $\ast_6 A = - J \wedge A$ for $A^{1,1}$ primitive $1,1$ complex form and $J$ k\"ahler form

Question

Given a 6 dimensional manifold, of complex dimension 3, take the Hodge star operator $\ast_6$ and a primitive (1,1)-form $A_2$ (i.e. such that $J \wedge \ast_6 A = J_{mn}A^{mn}=0$ and also $J\wedge J \wedge A = 0$). Show that

$\ast_6 A = - J \wedge A$

with $J$ the Kahler form.