git - Why Git ignores ~/.ssh/id_rsa, wants ~/.ssh/id_dsa or ~/.ssh/id_ecdsa?

Question

This is the error I'm receiving:

no such identity: /home/eduan/.ssh/id_dsa: No such file or directory
no such identity: /home/eduan/.ssh/id_ecdsa: No such file or directory
Permission denied (publickey).

That's what happens when I try to push, or in this case when I do ssh -T git@github.com.

I have correctly generated the id_rsa and id_rsa.pub files.

How may I go about solving this? I'm using Arch Linux with E17 BTW.

EDIT:
@kortix would the following work for this?:

Host github.com
    IdentityFile ~/.ssh/id_rsa

It doesn't seem to work for me yet... I get the following when I push with Git:

Permission denied (publickey).
fatal: Could not read from remote repository.

Please make sure you have the correct access rights
and the repository exists.

I made sure the repo exists, and I also updated the remote URL with git remote set-url origin git@github.com:Greduan/dotfiles.git.

I also added the SSH key to the list of accepted SSH keys in GitHub. What else should I do?