Commutative Associative and Distributive Laws

In ordinary scalar algebra, the additive and multiplicative operations obey the commutative, associative, and distributive laws as follows:

Commutative law of addition: Commutative law of multiplication: Associative law of addition; Associative law of multiplication: Distributive law:

a 4 b = b 4 a ah = ha (<t + b)+c = a+{h + c) (ab)c = a(bc) a(b 4 c) = ab 4 ac

These have been referred to during the discussion of the similarly named laws applicable to the union and intersection of sets. Most, but not all, of these laws also apply to matrix operations—the significant exception being the commutative law of multiplication.

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