Find the inverse of 5 under multiplication modulo 11 on Z₁₁

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

Example, 4 x₁₁ 9 = Remainder of (4 x 9) divided by 11

For bS to be an inverse of aS, 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.