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Find the identity element in the set of all rational numbers except – 1 with respect to * defined by a*b = a + b + ab
Given that binary operation ‘*’ is valid for set of all rational numbers Q defined by a*b = a + b + ab for all a,b∈R.
Let us assume a∈R and the identity element that we need to compute be e∈R.
We know that he Identity property is defined as follows:
⇒ a*e = e*a = a
⇒ a + e + ea = a
⇒ e + ae = a – a
⇒ e(1 + a) = 0
⇒ e = 0
∴ The required Identity element w.r.t * is 0.
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