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Given a set and a binary operation defined on the set,

the inverse of any element is that element which, when combined with the first, gives the identity element for the binary operation.

If the set is integers and the binary operation is addition, then the identity is 0, and the inverse of an integer k is -k.

If the set is rational numbers and the binary operation is multiplication, then the identity element is 1 and the inverse of any member of the set, x (other than 0) is 1/x.

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Q: What is inverse in algebra?
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