Binary operation: inverse question

Question

A subset of Q is given and a binary operation is specified. State whether the set has a unique inverse element. If not, write whether it has left inverse element, a right inverse element or neither for each element of set.

{-1,1},÷

Answer 1

No the inverse element is NOT unqiue

-1 has -1 as its inverse while 1 has 1 as its inverse.

In other words each element in this case is its own inverse.

The left and right inverses for -1 are -1 and -1

the left and right inverses for 1 are 1 and 1