Invertibility

https://en.wikipedia.org/wiki/Inverse_element https://en.wikipedia.org/wiki/Multiplicative_inverse https://en.wikipedia.org/wiki/Absorbing_element https://en.wikipedia.org/wiki/Additive_inverse https://en.wikipedia.org/wiki/Generalized_inverse

$(!\exists e, \ \forall x, \ \exists x^{-1}\in A)\ .\ x\star x^{-1} = e = x^{-1}\star x$