**(i) Consider e as an identity element.**

We know that a * e = a Ɐ a ∈ Q {1}

So a + e – ae = a

It can be written as

e (1 – a) = 0

So e = 0 ∈ Q {1}

a * 0 = a + 0 = a

So 0 * a = 0 + a = a

**Hence, 0 is the identity element in Q – {1}**

**(ii) Consider a ∈ Q – {1} where a **^{-1} = b

We know that a * b = 0

It can be written as

a + b – ab = 0

So a = ab – b

a = (a – 1) b

We get b = a/ a – 1 ∈ Q – {1}

So a ^{-1} = a/ a – 1 ∈ Q – {1}

**Therefore, each a ∈ Q – {1} has its inverse.**