Construct the composition table for _6 on set S = 0, 1, 2, 3, 4, … - Vidyadip

Question

Construct the composition table for $\times _6$ on set $S = {0, 1, 2, 3, 4, 5}$.

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Answer

Here,
$1\times _61$ = Remainder obtained by dividing $1 \times 1$ by $6 = 1$
$3\times _64$ = Remainder obtained by dividing $3 \times 4$ by $6 = 0$
$4\times _65$ = Remainder obtained by dividing $4 \times 5$ by $6 = 2$
So, the composition table is as follows:

$\times _6$	0	1	2	3	4	5
0	0	0	0	0	0	0
1	0	1	2	3	4	5
2	0	2	4	0	2	4
3	0	3	0	3	0	3
4	0	4	2	0	4	2
5	0	5	4	3	2	1

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