In first order logic, I have read that there are a couple of identity rules. 

 - If I have "a=b" does it mean that I can also write it as "b=a"? 
 - Is it true one-way or both? 
 - And if I have two statements such as "a=b" and "a=c". Can I derive both "b=c" or "c=b" from this?