$A$ is unitary iff $\langle Av,Av\rangle=\langle v,v\rangle$ over arbitrary field

Question

I am trying to show that $A$ is unitary iff $\langle Av,Av\rangle=\langle v,v\rangle$ when $A$ comes from an arbitrary field. That is, we are dealing with an arbitrary inner product space, so we only have the basic axioms of inner products (positive definiteness, conjugate symmetry, and linearity) at our disposal. That said, I'm not sure if we are able to use $\langle v,Aw\rangle=\langle A^*v,w\rangle$ since I don't know how to prove this without $\langle v,w\rangle=w^*v$ defined over $\mathbb{F}=\mathbb{C}$. Any hints?