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**What is operation?
where we used it in previous classes?**

**On the set Q of all rational numbers an operation * is defined by `a*b = 1 + ab`. Show that * is a binary operation on Q.**

**Number of binary operations**

**Commutativity of binary operations**

**Associativity of binary operations**

**Distributivity of binary operations**

**Definition and Theorem: Let * be a binary operation on a set S. If S has an identity element for *; then it is unique.**

**Invertible element
(definition and examples)**

**Let * be an associative binary operation on a set S with the identity element e in S. Then. the inverse of an invertible element is unique.**

**Let * be an associative binary operation on a set S and a be an invertible element of S. Then; inverse of a^-1 is a.**