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

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.

Quote:

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Originally Posted by adam_leeds

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

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What do YOU think for the second one?

Quote:

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Originally Posted by Drexel28

What do YOU think for the second one?

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it is a binary operation