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Question
Write the composition table for the binary operation ×5 (multiplication modulo 5) on the set S = {0, 1, 2, 3, 4}.
Solution
Here,
1 \[\times_5\] 1 = Remainder obtained by dividing 1 \[\times\] 1 by 5
= 1
3 \[\times_5\] 4 = Remainder obtained by dividing 3 \[\times\] 4 by 5
= 2
4 \[\times_5\] 4 = Remainder obtained by dividing 4 \[\times\] 4 by 5
= 1
So, the composition table is as follows:
| ×5 | 0 | 1 | 2 | 3 | 4 |
| 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 1 | 2 | 3 | 4 |
| 2 | 0 | 2 | 4 | 1 | 3 |
| 3 | 0 | 3 | 1 | 4 | 2 |
| 4 | 0 | 4 | 3 | 2 | 1 |
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