2 of 2 grammar, formatting

What exactly are the identity rules in logic?

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?