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In the group $(1,2,3,4,5,6)$ under multiplication $7,2^{-1} \times 4$ is equal to
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Verified Answer
The correct answer is:
$2$
We have,
$$
\begin{aligned}
& & 2 \times 4 &=1(\bmod 7) \\
\text { Hence, } & 2^{-1} &=4(\bmod 7) \\
\text { Now, } & 2^{-1} \times 4 &=4 \times 4=16 \\
\text { Now, } & 16 &=(2 \times 7)+2 \\
\therefore & 16 &=2(\bmod 7) \\
\Rightarrow & 2^{-1} \times 4 &=2(\bmod 7)
\end{aligned}
$$
$$
\begin{aligned}
& & 2 \times 4 &=1(\bmod 7) \\
\text { Hence, } & 2^{-1} &=4(\bmod 7) \\
\text { Now, } & 2^{-1} \times 4 &=4 \times 4=16 \\
\text { Now, } & 16 &=(2 \times 7)+2 \\
\therefore & 16 &=2(\bmod 7) \\
\Rightarrow & 2^{-1} \times 4 &=2(\bmod 7)
\end{aligned}
$$
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