You will have a problem connecting 9 LED's in series to work on 12VDC because the minimum voltage for some LED's is about 2VDC. Please post a schematic of the matrix, give the color. As I read your schematic, you want a - going pulse to light the LED's.
The base of the PNP transistor must be +11.5V or higher to turn it off. It never gets that so it never turns off.
When the input is +5V then the base is +11.3V and its base current is (11.3V - 5V)/1k= 6.3mA.
This circuit (T1) needs a 0 to 12 volt signal to turn it on/off. Your little computer can not do 12 volts.
This next circuit (2N3904) works well with a computer. (0/5V)