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Binary Operations — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsBinary Operations3 Marks
Question
Write the multiplication table for the set of integers modulo $5$.
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Answer

$Z_5 = {0, 1, 2, 3, 4}$
$a\times _5 b$ is the remainder when the product of ab is divided by 5.
The composition table for $\times _5$ on $Z_5 = {0, 1, 2, 3, 4}$​​​​​​​
$\times _5$​​​​​​​ 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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