Question

Construct the composition table for ×₅ on Z₅ = {0, 1, 2, 3, 4}.

Answer 1

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:

${\times }_5$	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