The triangle with vertices P = (0, 0), Q = (1, 0), R = (0, 2) is given.

1.Give an affine-linear mapping = id, which maps delta into itself, for which () = holds, explicitly in the form (x) = Ax + b!

2.How many mappings with this property are there? Show that the set of all maps from Part 1 (including the identity) forms a subgroup of the group of bijective, affine-linear maps.

Hint: Show that an affine linear map maps into itself if and only if ({P, Q, R}) = {P, Q, R}