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To prove the uniqueness of the multiplicative inverse of a real number, let's assume that there are two different multiplicative inverses, say a and b, for a given real number x. This means that a * x = b * x = 1. By multiplying both sides of the equations by the common factor x, we get a = b = 1/x, which proves that the multiplicative inverse is indeed unique.

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5mo ago
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8y ago

Suppose p and q are inverses of a number x. where x is non-zero.

Then, by definition, xp = 1 = xq

therefore xp - xq = 0

and, by the distributive property of multiplication over subtraction,

x*(p - q) = 0

Then, since x is non-zero, (p - q) = 0.

That is, p = q.

[If x = 0 then it does not have a multiplicative inverse.]

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Q: How do you prove the multiplicative inverse of a real number is unique?
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