There is an urban legend that if you do many LEDs you should multiplex them. If the LEDs are not high power, that is pure baloney.

as an example, let us take a 8*8 matrix

to multiplex, you need
a high side latch (8 I/O pins)
8 transistors for high side
a low side latch (8 I/O pins)
8 low side transistors (MPX = 8* the current)

non-multiplexed you need
8 shift registers from a family that has enough oomp to drive the leds (e.g. AHC 10mA (75ma/package), ALS 24mA 2221 50mA) and 3 I/O pins.

so the difference is
16 transistors and 17 I/O pins
or
6 registers and 3 pins.

That does not sound like a great trade (well it is not that bad) but add to the multiplexed method a) the siftware iverhead and b) what hardware you have to add because your matrix used up the I/O pins.

or, of course, you can use dedicated LED drivers such as the SITI ST2221A which will give yoi constant current drive.

Erik