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  4. In the group 1, 2, 3, 4, 5, 6 under multiplication modulo 7, 2-1 × 4

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

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Solution:

Here 1 is i.d. . eff
Since $2 \times 4 = 8 = 1$ (mod 7 ) $\therefore 2^{-1}=4$
$\therefore 2^{-1}\times 4=4 \times4 =2$ (mod 7)