Compute the Cayley table of $\mathbb{Z}^*_{10}$

Question

Could someone please help me with this question: Compute the Cayley table of the group $\mathbb{Z}^*_{10}$ and give an explicit definition for the different homomorphisms $\psi_1 ,$$\psi_2$$\quad$ $\mathbb{Z}^*_{10}$$\to$$\mathbb{Z}^*_{10}$.

Answer 1

Here are simple steps you may follow. 1.List the non zero element of modular 10 which are 1,2,3,4,5,6,7,8,9 . 2.Determine the value of gdc(k,n)=1 i.e gcd(1,10)=1 , gcd(2,10)=2,gcd(3,10)=1, gcd(4,10)=2,gcd(5,10)=5,gcd(6,10)=2,gcd(7,10)=1,gcd(8,10)=2,gcd(9,10)=1. 3.The elements you need to form the Cayley table are 1,3,7,9