I am trying to figure out these relations (Hodge operator acts on the following r-forms)

$\displaystyle *(dx\wedge dy)=dz$

this one I do not get

$\displaystyle *(dy\wedge dz)=dx$

$\displaystyle *(dx\wedge dx)=-dy$ how do they work?

They only way I can explain it is that the wedge product work like the cross product for example

$\displaystyle x\times y=z$

$\displaystyle x\times z=-y$ and so on

is it a correct way of thinking?