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in Binomial Theorem by (50.8k points)

For the binary operation ×10 set S = {1, 3, 7, 9}, find the inverse of 3.

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Given x10 set S10 = {1,3,7,9}

Now,

1 ×10 1 = remainder obtained by dividing 1 × 1 by 10

= 1

3 ×10 7 = remainder obtained by dividing 3 × 7 by 10

= 1

7 ×10 9 = remainder obtained by dividing 7 × 9 by 10

= 3

Therefore, the composition table is as follows:

x10 1 3 7 9
1 1 3 7 9
3 3 9 1 7
7 7 1 9 3
9 9 7 3 1

From, table it that elements of first row as same as the top-most row.

Therefore, 1 ∈ S is the identity element with respect to ×10

Let us find inverse of 3

3 ×10 7 = 1

Therefore, the inverse of 3 is 7.

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