Table of Contents

The majority of proofs of equations relies on either algebraic proofs, geometric proofs, or both to prove a theorem or equation.
Algebraic Proofs
A large majority of algebraic proofs result from the use of these properties:
Commutative Property
The commutative property states the arrangement of some multiplied or divided element does not affect the element output. In simple arithmetic:
(1)The commutative property does not always hold though. For example, the cross product of two vectors does not follow the commutative property:
(2)Therefore:
(3)Associative Property
The associative property states the arrangement of some added or subtracted element does not affect the element output.
For example with simple arithmetic:
(4)Or
(5)Distributive Property
The distributive property merges the commutative and associative property. For example with simple arithmetic:
(6)