BD = I D = B –1.
B is invertible and BZ = O Z = O.
AC + XZ = AC + O = I C = A –1.
Therefore if M is invertible then both A and B are invertible.
AY + XD = AY + XB –1 = O AY = –XB–1
Y = –A–1XB–1
Note that it follows from this result that, for any constant x and non-zero constants a, b,
 .
and 
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