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.