Simple example to describe Bilinear mapping Notation : $\mathbb{G}$ is an additive group and $\mathbb{G}_T$ is multiplicative group of prime order $q$.

Bilinear mapping $e: \mathbb{G} \times \mathbb{G}  \rightarrow \mathbb{G}_T$ has to satisfy two properties.

1) $e(aP,bQ) = e(P,Q)^{ab}$        for all $P,Q \in \mathbb{G} , a,b \in \mathbb{Z}_q$ 

2) $e(P,P) \ne 1_{\mathbb{G}_T}$ for all $P \in G$

In addition to the above two, it has to be computable.

Is there any simple example for such bilinear pairing?  

I searched over internet as I can but I didn't find. 

I want example like this $e(x,y) = xy \mod n$ (It's not a valid example).

Note: The sets under consideration $\mathbb{G},\mathbb{G}_T$ must have at least four elements.

Duplicate question for https://math.stackexchange.com/questions/1380004/simple-example-for-bilinear-mapping
A toy example would be this simple map with $\mathbb{G} = \mathbb{Z}/5$ to $\mathbb{G}_T = \mathbb{Z}^*/11$, as follows:

$$e(x,y) = 3^{xy} \bmod 11$$

It's easy to verify that both equations hold (except that $e(0,0) = 1$; that's actually a necessary consequence of the first equation, and so I'll consider that an acceptable exception).

Of course, even if you scale this up to non-toy sizes, this particular style of bilinear mapping isn't cryptographically interesting; however it does answer your question.