Question

In the group $G = \{1,5,7,11\}$ under multiplication modulo $12$, the solution of $ 7^{-1} \; \otimes_{12} (x \otimes_{12} 11) = 5$ is $x$ =

• A. 11
• B. 7
• C. 1
• D. 5

Answer 1

The Correct Option is C

Given that $G=\{1,5,7,11\}$ is a group under multiplication modulo 12 $\therefore 7^{-1}=7 $ $\left(\because 7^{-1} \otimes_{12} 7=1\right)$ Now, $7^{-1} \otimes_{12}\left(x \otimes_{12} 11\right)=5$ $\Rightarrow 7 \otimes_{12}\left(11 \otimes_{12} x\right)=5$ $\Rightarrow \left(7 \otimes_{12} 11\right) \otimes_{12} x=5$ $\Rightarrow 5 \otimes_{12} x=5$ $\Rightarrow x=1$