Question

In the group $G.=\{1,3,7,9\}$ under multiplication modulo $10$, the inverse of $3$ is

• A. 1
• B. 3
• C. 7
• D. 9

Answer 1

Answer: (C)

Given, $G=\{1,3,7,9\}$
Here, $1\times {}_{10}1=1,3\times {}_{10}1=3,7\times {}_{10}1=7$
$9{\times }_{10}1=9$
It is clear that 1 is the identity element. Since, $G$ is a group, then inverse of each element exist in $G$.
$\Rightarrow 3{\times }_{10}7=1=7{\times }_{10}3$
$\therefore 7\in G$ is the inverse of 3