help prove this. thanks

(2) Let X1, . .., In, yl, . .., Un be the usual coordinates for R2. Let A = C (R2), the algebra of smooth (i.e. infinitely differentiable) functions on R2n. The Poisson bracket on A is n of ag of ag {f,g} = ax: dyi ay: Ori i=1 Show that (A, {, }) is a Lie algebra