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

Question

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

✓

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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