Q70 / 180 · COMEDK 2013 · Mathematics

In the group $(1,2,3,4,5,6)$ under multiplication $7,2^{-1} \times 4$ is equal to

  • A
    $1$
  • B
    $4$
  • Correct answer
    C
    $2$
  • D
    $3$

Solution

We have, $$ \begin{aligned} & & 2 \times 4 &=1(\bmod 7) \\ \text { Hence, } & 2^{-1} &=4(\bmod 7) \\ \text { Now, } & 2^{-1} \times 4 &=4 \times 4=16 \\ \text { Now, } & 16 &=(2 \times 7)+2 \\ \therefore & 16 &=2(\bmod 7) \\ \Rightarrow & 2^{-1} \times 4 &=2(\bmod 7) \end{aligned} $$

Hence, the correct answer is option: 'C'.

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