Question

In the group $G=\{1,5,7,11\}$ under ${\otimes }_{12}$ the value of $7{\otimes }_{12}{11}^{-1}$ is equal to

(${\otimes }_{12}$: under multiplication modulo $12$)

• A. $5$
• B. $7$
• C. $11$
• D. $1$

Answer 1

Answer: (A)

$5$

Clearly ${11}^{-1}=11(\because 11{\otimes }_{12}11=1)$
$\therefore 7{\otimes }_{12}{11}^{-1}=7{\otimes }_{12}11=5$