See if following works for you.
First login to the Client say (A) . Type following command.
ssh –t –t -q 10.180.8.231 date
the above command displays date on Server(10.180.8.231)
(*)Add keygen to avoid prompting for password while running ssh command.
Type rsa-keygen –t rsa command at client.
When asked to save the file just press enter
[root@ABC-VMGR-51 .ssh]# ssh-keygen -t rsa
Generating public/private rsa key pair.
Enter file in which to save the key (/root/.ssh/id_rsa):
#by default the key is saved in /root/.ssh/id_rsa
Enter passphrase (empty for no passphrase):
Enter same passphrase again:
Your identification has been saved in /root/.ssh/id_rsa.
Your public key has been saved in /root/.ssh/id_rsa.pub.
The key fingerprint is:
Then ssh the id_rsa.pub file to remote server with the name as authorized_keys.