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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}.

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Solution

Here,

1×51 = Remainder obtained by dividing 1 × 1 by 5
= 1

3×54 = Remainder obtained by dividing 3 × 4 by 5
= 2

4×54 = Remainder obtained by dividing 4 × 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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