I have this excercise, I need your help on the third point:
i) Determine two integers $\alpha$ and $\beta$ such that $12\alpha + 7\beta = 1$
Answer: $\alpha = 3$ and $\beta = -5$
ii) Determine all the solutions of $7x\equiv 1 (mod. 12)$
Answer: $[-5]_{12} = \{-5+12k, k\in\mathbb{Z}\}$
iii) determine invertible elements (for product) for $(\mathbb{Z}_{12}, +, \cdot)$, and zero divisors
Answer: Here I need your help! How can I determine all invertible elements and all zero divisors?
iv) determine, if exists, a class $[a]\in\mathbb{Z}_{12}$ such that $[a][6]=[2].$
Answer: No, doesn't exist. $gcd(6,12)\neq 1$