General :: Ssh Login Without Password From Local To Remote And Further To Another Remove?

I know I can ssh login without password from a local to a remote. My question is how I can ssh without password from the remote to another remote. Say, I have three machines: A, B, C where A is the local machine. I use the same private/public key pair for all the login. What I can do are:

1. ssh from A to B.

2. ssh from A to C.

3. If I am sitting in the computer B (or B is local), then I can ssh from B to C.

What I am not able to do is:

After I ssh from A to B, I cannot ssh from the B to C. When I try to ssh from B to C, it asks me a passphrase.