Construct the composition table for _5 on Z_5 = 0, 1, 2, 3, 4 . - Vidyadip

Question

Construct the composition table for $\times _5$ on $Z_5 = {0, 1, 2, 3, 4}$.

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Answer

Here,
$1\times _51$ = Remainder obtained by dividing $1 \times 1$ by $5 = 1$
$3\times _54$ = Remainder obtained by dividing $3 \times 4$ by $5 = 2$
$4\times _54$ = Remainder obtained by dividing $4 \times 4$ by $5 = 1$
Therefore,
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

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