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.