1. ## Binary Operations, check please :)

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

2. 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: $\displaystyle 2^{\frac{1}{2}}$ 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
What do YOU think for the second one?

4. Originally Posted by Drexel28
What do YOU think for the second one?
it is a binary operation