Using two 74HC595 chips, we can control both the rows and columns of a LED matrix. Below shows them connected to a 5x5 display, but of course this can be expanded to an 8x8 display. Note that no resistors are used, as each LED will be switched on and off very fast no real damage should be caused to them. However, it may be a good idea to provide appropriate resistors to each column if you will be switching through each row in turn. The opposite applies for switching through each column.

 

 

Each row is connected to an output of the bottom IC1. Each column is connected to an output of the top IC2. I have kept all the inputs to the two chips seperate except for the enable line, although you could just as well connect the SCK, SCL and RCK inputs on each chip together.

 

To use this circuit, you would need to connect the the left inputs to the output ports on a microcontroller. To display something, you would first clock in the required data to both IC's using the Serial In and Ser_CLK inputs. One IC would have to be set to turn on just one row or column, with the other set to turn on the required LED's in that row or column as needed.

Then that data would be latched to the output by using the Ser_Latch (RCK) inputs (one of which I forgot to show), and set Ser_EN low to enable the outputs.

Then you would leave it display that for a small period of time (0.02 seconds for 50 Hertz) and then clock in the next row or columns data, repeating the whole process.