I'm having trouble understanding how two D-branes leads to a $U(2)$ gauge theory from [David Tong's](http://www.damtp.cam.ac.uk/user/tong/string.html) notes, chapter 7, pages 191-192. I am learning group theory and I understand that a 'charge' is a generator of the symmetry transformation, in this case $U(1)$ of $A\_{\mu}$. But now you have non Abelian gauge fields that are matrices and off-diagonal elements represent strings stretched between two different D-branes.

Here is what I do not understand:

1. Under the $U(1)$ symmetries transformation, the fields have $(A\_{\mu})^{1}\_{2}$ and $(A\_{\mu})^{2}\_{1}$ have charges $(+1,-1)$ and $(-1,+1)$ respectively. How do we know that this is true and what does this mean?
2. This implies that the gauge theory is $U(2)$. How does it follow from the above?