Let F,G be vector �fields on the plane such that both com-positions F dot� G, G dot� F : R^2 -> R^2 -> R^2 are the identity (x, y)->(x, y).

Question

Prove that the fi�eld F is incompressible if and only if G is incompressible.
(A vector fi�eld is called incompressible if its divergence is zero everywhere.)