Math Trivia : Find a fake coin

There are 9 coins and one of them is fake which is lighter than the others.
Find a fake coin using balance (with no scale and weight) 2 times

Divide 9 coins in 3 groups of A, B, and C with 3 coins in each group.

First, put 3 coins of A and B group on the balance.
<1>
If it is balanced, there is no fake in group A and B.
Then take 2 coins from group C to put on the balance.
If it is balanced, remaining one coin is fake.
If it is not balanced, the lighter coin is fake.

<2>
If it is not balanced with group A and B, take 2 coins from lighter group to put on the balance.
If it is balanced, remaining one coin is fake.
If it is not balanced, the lighter coin is fake.