b) is the set of all these linear transformations that are homomorphisms of . Let , then it has the form , by contrustion. We define a mapping as , the first coefficient. You need to show .
For each and in define a function by
The set of all such function forms a group with the group multiplication given by the compostion of the functions.(Not need to verify is a group)
a. Determine and find . Hence show that is non-abelian.
b. Show that ,given by , is a homomorphism.
I'm OK with the part but I forget how to show .
Also for part b, I don't really get it.
Thank you for help