Issue with Joomla! - Administrator links redirecting to site root

I was setting up a Joomla! site for a client when I kept having an issue with the Administrator site. Every link in the administrator areas would redirect me to /index.php. I just about went crazy trying to find the answer.

It turns out that the $live_site variable in the configuration.php file had a value in it. I set this variable to be a blank string and everything started working as it should.