How to install a battery in a Toyota Matrix?
It is no different than installing a battery in any car that has a regular 12 volt system. Make sure the vehicle is turned completely off. Take either a 10mm or 12mm open end wrench and loosen the terminal connections. Do the negative side first ( - ) and then the positive ( + ). If you are unsure of which is which, look on the side or top of the battery for the symbols. Most batteries have a tie down, so take your 12mm wrench and unscrew the nuts from the two rods coming up the side of the battery that are going through a bracket that spans the top of the battery. Remove the spanner and the cables from the terminal and pull it out. Put the new one in reverse order connecting the positive side last.
The stock roof-mounted antenna on the 2005 Toyota Matrix will unscrew from the antenna base that is attached to the roof. If your original antenna has been stolen, you should be able to obtain a replacement antenna and just screw it on the the antenna base that is still attached to the roof of your Matrix.