2006 toyota matrix

Here is a link to Bulldog Security for their wiring guide :  http://www.bulldogsecurity.com/bdnew/vehiclewiringdiagrams.asp

Looks like 2003 thru 2008 are the same, so here is a link to The12Volts listing :  https://www.the12volt.com/installbay/forum_posts.asp~TID~46272

Here is a link to DEI's listing  :  http://www.readyremote.com/main.asp?make=Toyota&model=Matrix

Not sure if all Matrix's had a transponder immobilizer system.  All the major bypass manufactures do list a module for that vehicle.  Check for any antenna ring at the ignition switch or get a plain $1.99 hardware store copy of the key and try it.