Q. In the group where is multiplication modulo , the identity element is
Solution:
Given,
The composition table is
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.
| 3 | 6 | 9 | 12 | |
|---|---|---|---|---|
| 3 | 9 | 3 | 12 | 6 |
| 6 | 3 | 6 | 9 | 12 |
| 9 | 12 | 9 | 6 | 3 |
| 12 | 6 | 12 | 3 | 9 |