I need to connect to hostB using user2 from hostA where I´m connected using user1.

I've run ssh-keygen -t rsa on hostA and copied the public key generated in ~/.ssh/id_rsa.pub to the ~/.ssh/authorized_keys of user2 in hostB.

Then I tried to connect from hostA to hostB using the command:

   $user1@hostA> ssh user2@hostB

I still get a request for password:

   user2@hostB's password:

If I try to connect using the same user on both hosts, it works correctly:

   $user1@hostA> ssh user1@hostB
   Enter passphrase for key '/home/user1/.ssh/id_rsa':

What am I missing?