A cyclic group is a special kind of group that has many similarities with modular arithmetic.

Task:

A. Prove that the cyclic group of order 3 is a group by doing the following:

1. State each step of your proof.

2. Provide written justification for each step of your proof.

B. Prove that the cyclic group of order 3 is isomorphic to Z3 under addition by doing the following:

1. State each step of your proof.

2. Provide written justification for each step of your proof.

**Subject Mathematics Abstract Algebra**