# Binary Operations, check please :)

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• Jan 8th 2010, 07:50 AM
adam_leeds
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
• Jan 8th 2010, 08:23 AM
Shanks
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: $2^{\frac{1}{2}}$ is a irrational number.
• Jan 8th 2010, 09:18 AM
Drexel28
Quote:

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

What do YOU think for the second one?
• Jan 8th 2010, 09:31 AM
adam_leeds
Quote:

Originally Posted by Drexel28
What do YOU think for the second one?

it is a binary operation