Maps act on column vectors, so the first element appears at the right of the product. Starting immediately before the focusing kick, one full cell has
(1)
Multiplying gives
(2)
It has , as required for this lossless linear beam optics. The other transverse plane experiences the opposite quadrupole signs, so
(3)
The two planes have different envelopes but the same trace and therefore the same stable phase-advance magnitude for this equal-strength doublet.

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