  We obtain the reflection matrices for the scattering of elementary magnons
from certain open boundaries, corresponding to open strings ending on D7 and D5
branes in $AdS_5\times S^5$. In each case we consider two possible orientations
for the vacuum state. We show that symmetry arguments are sufficient to
determine the reflection matrices up to at most two unknown functions. The D7
reflection matrices obey the boundary Yang Baxter-Equation. This is automatic
for one vacuum orientation, and requires a natural choice of ratio between two
unknowns for the other. In contrast, the D5 reflection matrices do not obey the
boundary Yang Baxter-Equation. In both cases we show consistency with the
existent weak and strong coupling results.
