Question

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

• A. $1$
• B. $4$
• C. $2$
• D. $3$

Answer 1

Answer: (C)

$2$

Under multiplication modulo 7, inverse of 2 is
$2\times 4=1\left(mod7\right)$
Hence
$2^{-1}=4$
Now
$2^{-1}\times 4$
$=4\times 4$
$=16$
Now
$16=(2\times 7)+2$
Hence dividing 16 by 7 gives a remainder 2.
Therefore answer is '2'.