Question

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

• A. 5
• B. 7
• C. 11
• D. 1

Answer 1

Answer: (A)

5

Answer 2

$G = \\{1, 5, 7,11\\}, \oplus_{12}$
we know that 1 is an identity element.
inverse of 11 is,
$11 \oplus_{12} 11^{-1} = 1$ and $11 \oplus_{12} 11 = 1$
Hence $11^{-1} = 11. \therefore \, 7 \oplus_{12} 11^{-1} = 7 \oplus_{12} 11 = 5$