1. ## [SOLVED] affine geometry

hey all,
i have been given this question and i dont have a clue where to start

For any subset ¬
of the affine plane R2, let G(¬) denote the group of all affine transformations

f
of R2 such that f(¬) = ¬.

1)Find all the elements of the group G = G(¬), where ¬is the hyperbola xy = 1

in R2.

thanks