Question -
Answer -
Let e be the identityelement in I+ with respect to * such that
a * e = a = e * a, ∀ a ∈ Q – {-1}
a * e = a and e * a =a, ∀ a ∈ Q – {-1}
a + e + ae = a and e +a + ea = a, ∀ a ∈ Q – {-1}
e + ae = 0 and e + ea= 0, ∀ a ∈ Q – {-1}
e (1 + a) = 0 and e (1+ a) = 0, ∀ a ∈ Q – {-1}
e = 0, ∀ a ∈ Q – {-1} [because a not equal to -1]
Thus, 0 is the identityelement in Q – {-1} with respect to *.