Given a differential form
$$x\,dy\wedge dz-y\,dx\wedge dz+z\,dx\wedge dy$$
I am supposed to prove that the it's pullback by a linear map of determinant one leaves it invariant. For example, if $\phi$ is a linear map and $\omega$ is a differential form then $\phi^*\omega=\omega$. Also, I was wondering, can we also say that any differential 2-form that is invariant under pull back of $\phi$ is scalar multiple of $\omega$?
I know the definition that for a linear map, we have that $\phi^*\omega(V)=\omega(\phi(V))$ but I don't know how to proceed.