Commutative Law of Multiplication

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Theorem

On all the standard number systems:

natural numbers $\N$
integers $\Z$
rational numbers $\Q$
real numbers $\R$
complex numbers $\C$

the operation of multiplication is commutative:

$a \times b = b \times a$


Proof

This is demonstrated in these pages:

Natural Number Multiplication is Commutative
Integer Multiplication is Commutative
Rational Multiplication is Commutative
Real Multiplication is Commutative
Complex Multiplication is Commutative

$\blacksquare$


Sources