Multiplicative inverse

Question

Every real number except zero has a multiplicative inverse

Are both the statements same?

$ ∀x((x != 0) → ∃y(xy = 1)) $

$ ∀x ∃y ((x != 0) → (xy = 1)) $

Comments

thank you

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Can anyone tell me if domain of y={1/2, 2/4, 3/6 }  and x={2}   then would the above 2 statements still be true?

I mean 1/2, 2/4, 3/6 all considered same?

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hey @prasant what if the inverse is not unique, then they both are different? suppose xy=100