Question

Write the composition table for the binary operation multiplication modulo 10 (×₁₀) on the set S = {2, 4, 6, 8}.

Answer 1

Here, 

2 \[\times_{10}\]  4 = Remainder obtained by dividing 2 \[\times\] 4 by 10
             = 8

4 \[\times_{10}\] 6 = Remainder obtained by dividing 4 \[\times\] 6 by 10
             = 4

2  \[\times_{10}\] 8 = Remainder obtained by dividing 2 \[\times\] 8 by 10
             = 6

3 \[\times_{10}\] 4 = Remainder obtained by dividing 3 \[\times\] 4 by 10
             = 2

So, the composition table is as follows:

×10	2	4	6	8
2	4	8	2	6
4	8	6	4	2
6	2	4	6	8
8	6	2	8	4