Q:

Group of rational numbers

The set $\mathbb{Q1}$ of all rational numbers other than 1 will form a group under the operation $a*b=a+b-ab$
If we consider another set $\mathbb{Q}$ of all rational numbers.Will the set of rational numbers $\mathbb{Q}$ form a group under the same operation? Looks like This set satisfies the properties of group under the above operation !

A:

What is the inverse of $1$ under this group operation? There isn't one: $1 * b = 1+b-b=1 $ for any $b$.

