Question

Write the composition table for the binary operation ×₅ (multiplication modulo 5) on the set S = {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:

×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