I'm having a little trouble with the difference between my notes and my textbook notation.

I have

I have to determine the orders of and , and whether and are isomorphic.

For the first part I have

So they have order 4. Correct?

For the isomorpic part can I just find a 2x2 matrix that shows that isn't a homomorphism?

Do I even know what I'm talking about? (just started group theory last week)