When an operation ‡ is defined in a set E, the inverse of a non-zero element x of E is an element denoted by \(n^{-1}\), such that n ‡ \(n^{-1}\) = 1.
Example
- The inverse of \(\dfrac{4}{9}\) is \(\dfrac{9}{4}\), since \(\dfrac{4}{9}\space × \space\dfrac{9}{4}\space = \space 1\).
- Consider the set E = {a, b, c} and the union set operation denoted by \(\bigcup \). We have {a, b} \(\bigcup\) {a, b}’ = E, where E is the identity element for the operation of union.