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The identity element for multiplication of numbers is 1 and it has the property that for any number, X, in the number system,

X * 1 = X = 1 * X

The multiplicative property of -1 is

X * (-1) = -X = (-1) * X for sets where -1 and -X are defined: they need not be, eg in the set of positive numbers.

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Q: What is the differences between the identity property of multiplication and the multiplicative property of -1?
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