Question

Let f:Rn -> Rn and g:Rn -> Rn be inverse functions. Suppose f and g are differentiable. Show that determianants of Df and Dg are not zero, and that Dg=(Df)^-1. Where Df and Dg is the derivative of f and g respectively.

Answer 1

btw, (Df)^-1 means the inverse matrix of Df