If you don't mind a bit of algebra, you could write the equations in terms of their real and imaginary parts:

   M A = B
  (Re M + i Im M) (Re A + i Im A) = (Re B + i Im B)
  (Re M) (Re A) - (Im M) (Im A) = Re B
  (Re M) (Im A) + (Im M) (Re A) = Im B
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The latter two equations are two coupled (real) equations for the unknowns Re A and Im A, which you can solve for using Math::MatrixReal as in your example.

Update: You could write these two coupled equations as one matrix equation:

   / Re M    -Im M  \  / Re A \     / Re B \
   |                |  |      |  =  |      |
   \ Im M     Re M  /  \ Im A /     \ Im B /
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and then use Math::MatrixReal as before.