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Consider the group G = (1,2,3,4,5,6) under multiplication modulo 7 a) Find multiplication table of G b) find Inverse of every element
written 7.3 years ago by gravatar for teamques10 teamques10 ★ 64k modified 2.2 years ago by gravatar for pedsangini276 pedsangini276 • 4.7k

Mumbai University > Computer Engineering > Sem 3 > Discrete Structures

Marks: 8 Marks

Year: May 2015
discrete mathematics
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written 7.3 years ago by gravatar for teamques10 teamques10 ★ 64k

We have G={1, 2, 3, 4, 5, 6}

The composition table is as follows:

$\oplus$ 1 2 3 4 5 6
1 1 2 3 4 5 6
2 2 4 6 1 3 5
3 3 6 2 5 1 4
4 4 1 5 2 6 3
5 5 3 1 6 4 2
6 6 5 4 3 2 1

From the table, we see that $\oplus$ is a binary operation on G.

Hence from the above table it is being observed that the inverse of 1, 2, 3, 4, 5, 6 are respectively 1, 4, 5, 2, 3, 6.
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