Simple example to describe 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.