Write the composition table for the binary operation ×5 (multipli… - Vidyadip

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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Answer

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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