Please do not implement that circuit it will burn both the arduino and the LEDs.
You can't connect an LED direct to pin 13 without a current limiting resistor or you will destroy something, maybe not immediately but damage will be done instantly.
The same goes for the LEDs in the matrix. You need drivers and current limiters.
This page shows you the basics of driving a matrix:-
http://www.thebox.myzen.co.uk/Workshop/LED_Matrix.html
You need to do a lot more learning until you are ready to start this project.