# Automorphism proof

Please show all work. Thanks

See attached

Task:

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 ?

https://brainmass.com/math/linear-transformation/automorphism-proof-210872

#### Solution Summary

This provides an example of an automorphism proof.

$2.19