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Element Functions
Function Inverses
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Integer Additive Inverses
Rational Multiplicative Inverses
Real Matrix Inverses
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Inverse Elements


Is the inverse of an element function the element function of a different element?


The inverse of an element of an algebra (also called the inverse element) is the element (if it exists) whose corresponding element function under the operation is the inverse of the first element's function.


Let $(A, +)$ be an algebra. Let $a \in A$. If the inverse element for $a$ exists and is unique we denote it by $\inv{a}$. In other words $+^{\inv{a}} \circ +^{a} = \idfn{A}$

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