Question

In the group $\left(G,{\otimes }_{15}\right)$, where $G=\{3,6,9,12\},{\otimes }_{15}$ is multiplication modulo $15$, the identity element is

• A. 3
• B. 6
• C. 12
• D. 9

Answer 1

Answer: (B)

Given, $G=\{3,6,9,12\}$
The composition table is

$x_{15}$	$3$	$6$	$9$	$12$
$3$	$9$	$3$	$12$	$6$
$6$	$3$	$6$	$9$	$12$
$9$	$12$	$9$	$6$	$3$
$12$	$6$	$12$	$3$	$9$

From the table $6$ is the identity element.