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Question
Let * be a binary operation on Z defined by
a * b = a + b − 4 for all a, b ∈ Z Find the identity element in Z ?
Solution
Let e be the identity element in Z with respect to * such that
\[a * e = a = e * a, \forall a \in Z\]
\[a * e = a \text { and }e * a = a, \forall a \in Z\]
\[a + e - 4 = a \text{ and }e + a - 4 = a, \forall a \in Z\]
\[e = 4 , \forall a \in Z\]
Thus, 4 is the identity element in Z with respect to *.
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