Call for author posts url and/or help with rel="author"

So I’m trying to create a link to each author on both the home page and each post of Automoblog.net to the author’s post URL but also include rel=”author” in there. It’s not working for me.

I can’t simply call the URL without the link. Codex says get_the_author_posts_url() works, but it doesn’t. I’m using the_author_url() temporarily, which links to the URL they have in their profile, but I want it to link to the author archive.

Here’s the code I’m using:

<a rel="author" href="<?php the_author_url(); ?>" style="text-decoration:none;"><?php the_author(); ?></a>

Am I doing something wrong?

Thanks so much for any help.