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.
I think that there are something missing that I do not understand.
Thank you for your help.