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Binary Operations — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsBinary Operations2 Marks
Question
Write the composition table for the binary operation $\times _5$ (multiplication modulo $5$) on the set $S = {0, 1, 2, 3, 4}$.
✓

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 $5 = 1$
So, 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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