Please show all work. Thanks
Prove the following theorem:
is an automorphism of under componentwise addition.
Additional Notes on the Task:
Be careful not to confuse the homomorphism's action as a function with the group operation's action as componentwise addition.
is componentwise addition where and in . How would you show the function is a morphism using X, Y, and X + Y ?
This provides an example of an automorphism proof.