How to establish "ssh" trusted hosts between PCs with non-root users?
 

When using root, I can establish trusted hosts with localhost.
But when i do the same thing using non-root users, it can't be done.
Why?

Please describe, in detail, exactly what you are trying to do, and exactly, step by step, what you have so-far done or attempted to do.

When you say, "establish ssh trusted hosts," please cite a web-page that refers specifically to what you are talking about when you use that phrase.

When you try it as a non-root user and "encounter a roadblock," please detail exactly what message you get, and why you come to the conclusion that it is an insurmountable obstacle.

As you can see from my italics, "the devil is in the details" for providing the most-useful answer to your question.

when i run following sequence of instructions as root, i can establish trusted hosts with "localhost":

ssh-keygen -t rsa
cd $HOME/.ssh
cat id_rsa.pub >> authorized_keys

But when i run these instructions as a non-root users, i can't get the trusted hosts authentication. Why?

The public key for the user on the client needs to be added to the user's ~/.ssh/authorized_keys file on the server. You added the client's public key to the client's authorized_keys file instead.

The server's /etc/ssh/sshd_config file also needs to be configured so that pubkey authentication is used. It's possible the server is configured so that only root uses pubkey authentication.