I think the key statement in the link @folkertdev provides that refutes your ‘inverse’ definition is that “0 does not have a multiplicative inverse”, so does not apply in this case.
I was always taught at school that the division operator is simply undefined for a denominator of 0, so any argument that states what the “mathematical” value should be is dubious at best. Better I think is to evaluate the implications of assigning a value (0 in the case of Elm’s //0) for this undefined operation, as @folkertdev’s link does.