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0 is the additive identity of Q. And you can have 1 and only 1 additive identity.
[1,1] is better written as just 1. The only rational number that doesn't have a multiplicative inverse is 0. Consider a/b where a and b are integers and a and b are nonzero. Then a/b * b/a = 1, and thus, all nonzero rationals have a multiplicative inverse.
I need to prove that every element of Q (rational numbers) has an inverse with respect to addition. From what understand, I need to use the fact that [0,1] is the additive identity of Q. However, I have no idea what to do beyond that.