i believe all the information was in the first post....
Not even close, but never mind, we are getting there!
You are correct to point out that multiplexing an led matrix is indeed a form of persistence of vision display.
I can see that you added only 3 resistors. This will mean using a 1 in 9 multiplex ratio. This will probably be ok, but the brightness may not be very consistent between the different colours, and the overall brightness may not be enough to see well in very bright light. If you are not happy with the brightness, you may have to remove those resistors and replace them with 9, on the anodes rather than the cathodes. This will allow a 1 in 3 ratio, which will be considerably brighter, and allow you to use different resistor values for each colour to achieve a more even brightness.
Next question: what kind of transistors are you using? I don't see them on the board. Without them, you will overload and damage the Arduino pins when you try to light more than one led at once.
Also, why is there a 30 pin header on the board? It should need only 12 pins. As wvmarle said, a schematic would be helpful.