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)

7

Answer 2

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