OpenSSH Passwordless Authentication between 2 systems with different UID's

How to communicate without a passwd between 2 Unix systems where
the communicating sessions have different uid/s? (NOTE: both systems
are on OpenSSH)

e.g.

SystemA UserA SSH to SystemB UserB

Here is what I tried but failed.

As UserA in System A:
ssh-keygen -t dsa
cd ~/.ssh
cat id_dsa.pub > authorized_keys2
scp ./id_dsa.pub UserB@SystemB:.ssh/. (when prompt for the passwd, I typed UserB's passwd)

As UserB in System B:
cd .ssh
cat id_dsa.pub > authorized_keys2

Same trick for same user ID would work in the above example (i.e.
SystemA UserA SSH to SystemB UserB)

Could someone please shed some light here? Thank you very much!

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