This abstract algebra problem seems trivially easy. Did I overlook something?

[jdinatale]

Homework Statement

The problem seems too easy so I suspect that I am overlooking something important. A problem this easy would be completely out of character for my professor...

 

[vela]

You've shown it's a homomorphism, but it asked you to show it's an isomorphism.

 

[jdinatale]

You've shown it's a homomorphism, but it asked you to show it's an isomorphism.

Whoops! That's a typo. I typed the question wrong in latex. The problem on the assignment sheet says homomorphism.

So assuming that the problem is asking for a homomorphism, does it look legit?

 

[vela]

Looks fine to me.