# Q- Let S be a set on which an associative binary operation · has been defined such that S contains an identity element eS. Let U(S) be the set of all the units in S. Prove that U(S) is a group with respect to the operation ·. It is called the group of units of S.

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Q- Let S be a set on which an associative binary operation · has been defined such that S contains an identity element eS. Let U(S) be the set of all the units in S. Prove that U(S) is a group with respect to the operation ·. It is called the group of units of S.

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Step 1

To verify that U(S) satisfies the axioms of a group (under the given conditions)

Step 2

For notational simplicity , we simply write e and U , instead of e(S) and U(S). U is just the set of all invertible elements of ...

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