Why Does Multiplying Jacobian Determinants Equal One?

[primrosewater]

Homework Statement

Prove that J(s,t/x,y)*J(x,y/s,t)=1 (Hint: Multiply the determinants).

Homework Equations

Definition of a Jacobian.

The Attempt at a Solution

I found the determinants and multiplied them. Now I have a FOILed equation of partial derivatives and no idea where to go from there. If I'm missing some underlying mathematical fact involving partials or Jacobians that everyone "knows," I'd appreciate it if someone would tell me anything at all. I don't know where to go beyond the hint at all.

 

[gabbagabbahey]

$$\frac{\partial a}{\partial b}\frac{\partial b}{\partial a}=1$$

Does that help?