1. Ordinary addition and multiplication over the set of real numbers R are associative while
subtraction is not associative.
2. Matrix addition is associative over the set of all matrices of order m×n. Matrix multiplica-
tion is associative over the set of square matrices of order n.
3. Vector addition is an associative binary operation over the set of vectors V.
Distributive Laws: Let a set S have two binary operations, for example addition and multiplication
denoted by (+) and (.) defined over it. Then multiplication is said to be distributive with respect
to addition if
a.(b+c) =a.b+a.c(Left distributive law)
(b+c).a=b.a+c.a(Right distributive law)
Addition is distributive with respect to multiplication ...
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