Hello.

My discrete mathematics course has just started, so I'm not very good even at probably fairly easy things:

Prove if $\displaystyle \displaystyle \[G = A \times B\]$ is a bijection between finite sets $\displaystyle \displaystyle \[A\]$ and $\displaystyle \displaystyle \[B\]$ then $\displaystyle \displaystyle \[\left| A \right| = \left| B \right|\]$.

It looks pretty obvious because of the nature of this bijection, but I just can't seem to figure out notations to prove it in a mathematical way.

Thanks.