Question

In the group $\{1,2,3,4,5,6\}$ under multiplication mod $7,2^{-1}\times 4=$

• A. $1$
• B. $4$
• C. $2$
• D. $3$

Answer 1

The correct option is C $2$

In the given group under multiplication mod $7$, $1$ is the identity

Now, $2\times 4=8\equiv 1\left(mod7\right)⟹2\times 4\equiv \left(mod7\right)⟹2^{-1}=4$

Consider, $2^{-1}\times 4$

$=4\times 4=16$

But $16\equiv 2\left(mod7\right)$

$⟹2^{-1}\times 4\equiv 2\left(mod7\right)$

Hence, option C is correct.