Step 1:

Let $G=\{[1],[3],[4],[5],[9]\}$

Consider $(G,._{11})$

Drawing up the multiplication table,we have

Step 2:

Closure :All the products in the table belong to $G$.Closure is satisfied.

Associativity : Modular multiplication is associative.Since multiplication of integers is associative.

Existence of identity :From the table,it is evident that [1] is the identity element.

Existence of inverse: From the table it can be seen that the inverse of [1] is [1],$[3]^{-1} $ is [4],$[4]^{-1}$ is [3],$[5]^{-1}$ is [9] and $[9]^{-1}$ is [5].All the elements of $G$ have inverse in G.

The four group axioms being satisfied.,$(G,._{11})$ is a group.

Step 3:

Commutative property : Modular multiplication is commutative since multiplication of integers is commutative.

$\therefore (G,._{11})$ is an abelian group.