the first one is binary operation since complex field contains real number filed as a subfield.
the last one is not binary opration, a counterexample: is a irrational number.
Ordinary Multiplication on complex numbers
not a binary operation because to complex numbers multiplied together gives a real number e.g 3i x 2i = -6
Matrix multiplication on the set of all 2x2 non-singular matrices with real elements.
binary operation
p*q = p/q p,q belong to Q\{0}
binary operation
p*q = p^q p,q belong to Q
binary operation