# Binary Operations, check please :)

• Jan 8th 2010, 06:50 AM
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, 07:23 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: $\displaystyle 2^{\frac{1}{2}}$ is a irrational number.
• Jan 8th 2010, 08:18 AM
Drexel28
Quote:

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, 08:31 AM