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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