I have built an LED matrix (9x9) and want to run it with Arduino. I am using technique of scanning, lighting up 1 LED at 1 time.

The more I am reading about power requirements of a matrix the more I am getting confused. As per my understanding, there will only be 1 LED lit at any given time (and it will remain lit for a delay of 300ms). Therefore, I need to calculate voltage and current limiting resistor according to just 1 LED. 1 resistor will be attached with each row. Some articles are suggesting that it needs to be calculated for 1 whole row...WHY? I cant digest the logic.

Please note that I do not intend to use any shift registers or current sink devices. Arduino alone. As also depicted in Arduino CookBook and certain other resources.