How to avoid giving passwords in linux servers while logging in

Say, for example im in 10.10.10.1  machine and i need to login to 11.11.11.1 machine.

In source machine (10.10.10.1)
Login to the machine as root

#ssh-keygen -t dsa

#scp /root/.ssh/id_dsa.pub 11.11.11.1:/tmp

Now, go to destination machine (11.11.11.1).
Login to the machine as root

#mkdir .ssh
#cat /tmp/id_dsa.pub >> /root/.ssh/authorized_keys
#chmod 700 /root/.ssh/
#chmod 600 /root/.ssh/authorized_keys

Now try logging in ssh from 10.10.10.1 machine to 11.11.11.1 , you will not be prompted for password.
This will be useful in cases where we schedule backups from one machine to the other in cron job. So that files will be copied automatically without asking for the password.

Let me know, if anyone have any doubts on this.