The set of all rational numbers other than $1$ forms a commutative group with respect to the operation $*$ defined by $$a * b = a + b - ab$$ for all $a, b \in \mathbb{Q} \setminus \{1\}$.
How do I verify that
$$( a * b )^{-1} = a^{-1} * b^{-1}?$$
2026-04-09 06:02:22.1775714542
Proving identity for $\Bbb Q\setminus \{1\}$ with operation $a*b=a+b-ab$
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