Question

Find the inverse of 5 under multiplication modulo 11 on Z₁₁.

Answer 1

A composition table consists of elements which are a result of an operation on the set elements.

Here we have the operation, a x₁₁ b = remainder of ab divided by 11 where a, b ∈ S.

For b ∈ S to be an inverse of a ∈ S, a x₇b = e, where e is the identity element.

We know for multiplication operation we have the identity element as 1. 

So e = 1. 

For a = 5, 

5 x₁₁ (inverse of 3) = 1

From the table above, 5 x₁₁ 9 = 1.

Hence, i = 9.