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In the group $\left(G, \otimes_{15}\right)$, where $G=\{3,6,9,12\}$, $\otimes_{15}$ is multiplication modulo 15 , the identity element is
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The correct answer is:
6
Given, $G=\{3,6,9,12\}$
The composition table is
\begin{array}{c|cccc}
x_{5} & 3 & 6 & 9 & 12 \\
\hline 3 & 9 & 3 & 12 & 6 \\
6 & 3 & 6 & 9 & 12 \\
9 & 12 & 9 & 6 & 3 \\
12 & 6 & 12 & 3 & 9
\end{array}
From the table 6 is the identity element.
The composition table is
\begin{array}{c|cccc}
x_{5} & 3 & 6 & 9 & 12 \\
\hline 3 & 9 & 3 & 12 & 6 \\
6 & 3 & 6 & 9 & 12 \\
9 & 12 & 9 & 6 & 3 \\
12 & 6 & 12 & 3 & 9
\end{array}
From the table 6 is the identity element.
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