Can't rebind Ctrl-B to Ctrl-A in tmux

This config works for me. You probably haven't restarted your tmux server yet.

From man 1 tmux:

In tmux, a session is displayed on screen by a client and all sessions are managed by a single server. The server and each client are separate processes which communicate through a socket in /tmp.

One method is to terminate everything inside tmux, so tmux ls yields "no server running …". At this moment the next tmux command will start it anew, loading your new config file.

Also read this: Tmux not sourcing my .tmux.conf. According to one of the answers, this should work without the need of restarting the server:

This can also be done from within tmux, by pressing Ctrl+B (prefix key) and then : to bring up a command prompt, and typing:

source-file ~/.tmux.conf