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On the Set Z of Integers, If the Binary Operation * is Defined by a * B = a + B + 2, Then Find the Identity Element. - Mathematics

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प्रश्न

On the set Z of integers, if the binary operation * is defined by a * b = a + b + 2, then find the identity element.

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उत्तर

Let e be the identity element in Z with respect to * such that

\[a * e = a = e * a, \forall a \in Z\] 
\[a * e = a \text{ and }e * a = a, \forall a \in Z\] 
\[a + e + 2 = a \text{ and }e + a + 2 = a, \forall a \in Z\] 
\[e = - 2 , \forall a \in Z\]

Thus, -2 is the identity element in Z with respect to *.

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अध्याय 3: Binary Operations - Exercise 3.3 [पृष्ठ १५]

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आरडी शर्मा Mathematics [English] Class 12
अध्याय 3 Binary Operations
Exercise 3.3 | Q 4 | पृष्ठ १५

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