If $a^2 = b$ in a ring $R$ with unit, $a$ is invertible if and only if $b$ is and then $b^{-1} = (a^{-1})^2$. (Tell if this is clear to you, if not, I'll detail in an edit.) Apply this to $R = \mathbf{Z} / n \mathbf{Z}$. Apply the latter to the case $n = p$ is prime. ;-)

Detail. If $a$ is (for instance left) invertible of left inverse $c$ then $ca = 1$ so that $ca^2 = a$ which implies that $c^2 a^2 = ca = 1$, that is $c^2 b = 1$ and $b$ is invertible. If $b$ is (let's say left) invertible then $db=1$ and then $(d a) a = 1$ and $a$ is left invertible. Same for right inverse. The relation $c^2 a^2 = 1$ shows you the assertion on quadratic residue, that is, that if you are invertible and a quadratic residue, that you your inverse is also a quadratic residue.

If $a$ is a quadratic residue of odd prime $p$, then is it the case that $a^{-1}$ is also a quadratic residue?
I can't find much on how to set up any kind of establishments that are for charity. HOw would I go about this? Acquiring a building, a few volunteers, how much to run it per day, ect? Anyone have any experience in this? My character is a NG Druid, who had never been to a city and saw the poverty and lack of food and housing for people. He wants to help! But I have no idea on how to establish a continual act of help. Buying food for the town and stuff, one time is easy to figure out. How many people * ammount of food needed is the price. But for bigger acts of continual charity, who knows? 

EDIT:
So, it was suggested that I make an eco orphanage in a forest. I accidently doomed the continent with demons, so that won't work. (Wish spell to get rid of orcs, things went horribly wrong) NO one knows it was me though! :D 

I don't want the leadership feat cause I need my 6th level feat for a prestige class.

Also, I don't want to donate to the churches in this city, I'm finding a lot of corruption in some of these churches, especially this city, so I want something more controllable by me. 
