Sharing an SSH key between multiple users?

Cross posted from /r/linux

I have three users that needs to be able to SSH to another server using an SSH key. I've created a key and as user A I can make an SSH login by doing

ssh user@server -i /path/to/key 

If I have user B run the same command I get an error about not being able to read the private key. I made a group, and put users A, B, and C in the group and chmod 640 the private key.

Now SSH complains that the permissions on the key are incorrect, but ONLY for the user that owns the key. What is the best way to allow three users access to the same SSH key?

My ghetto solution was to have root "own" the key, so it only complains if root tries to use the key. This allows users A, B, and C to use the key without issue.