For the binary operation set , find the inverse of 3 .

Solution:

Here,
remainder obtained by dividing by 10

remainder obtained by dividing by 10

remainder obtained by dividing by 10

Therefore, the composition table is as follows:

It is observed from the table that elements of first row is same as the top-most row.
Therefore, is the identity element with respect to
We now have to find the inverse of 3

As a result, the inverse of 3 is 7 .