LED matrix : common anode vs common cathode is there a difference?

Alas it's not a simple job of swapping the anode/cathode (segment/digit) wires over at the fundamental way the LED's are wired to each other must also be changed or the LED's must be individually turned round.

Look at this image
Swapping segment and digit will not work because the LED is a one way device. Because it's a matrix though the Anodes and Cathodes are both common to each other.