I have investigated this thoroughly.
I use the Poincare sphere (also called Scheiber sphere) to compare the systems.
I represent the sound image locus with a circle around the listener.
Most of the regular matrix systems (SS, HF, DQ, EV4, QM, QX, QS, DS, PL, PLII) can be played on each other's decoders with only minor shifts of side images forward or backward. The circle shown is for Dolby Surround. I mix using the same circle.
The next matrix to appear was SQ.
Playing an SQ record through an RM decoder places the F and B signals in the same places. LF to straight L, and RF to straight R. LB and RB seem to be in the center of the room (all speakers equal amplitude).
Playing an RM record through an SQ decoder actually places most of the RM directions in nearly the correct direction. The F, LF, RF, and B signals always work the correct way, making these images. Since RM records do not produce SQ LB or RB signals, both back signals are the same
UMX/BMX is very different from the previous systems. The left and right is set by L and R channel amplitude in both RM and UMX. But RM uses inphase vs antiphase to control front to back image location. UMX uses 90 degrees L lead R for front and 90 degrees L lag R for back. Thus there is no front-back compatibility between RM and UMX.
However, you can use an SQ decoder to play UMX. Place the LF speaker to L, the RF speaker to R, The LB speaker to F, and the RB speaker to B. Also reverse the phase of the LB speaker.
Matrix H is halfway between RM and UMX, with 45 degree phase instead of 90 degree..
H plays on RM with reduced F-B separation.
H plays on UMX with reduced F-B separation.
RM plays on H with reduced F-B separation.
UMX plays on H with reduced F-B separation.
Ambisonics is close to RM and each can play on the other with slightly reduced F-B separation.