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:

${\times }_{10}$	2	4	6	8
2	4	8	2	6
4	8	6	4	2
6	2	4	6	8
8	6	2	8	4