COMEDK · Maths · 20. Sets and Relations
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 6
- B 3
- C 9
- D 12
Answer & Solution
Correct Answer
(A) 6
Step-by-step Solution
Detailed explanation
The composition table is \begin{array}{lllll} \hline 15 & 3 & 6 & 9 & 12 \\ \hline 3 & 9 & 3 & 12 & 6 \\ \hline 6 & 3 & 6 & 9 & 12 \\ \hline 9 & 12 & 9 & 6 & 3 \\ \hline 12 & 6 & 12 & 3 & 9 \\ \hline \end{array} From the table 6 is the identity element.
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