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## Solution to Mathematics for Machine Learning Exercise 2.1

We consider $(\mathbb R\setminus \{-1\},\star)$, where $$\label{2.1.1}a\star b:= ab+a+b,\quad a,b\in\mathbb R\setminus \{-1\}$$ a. Show that $(\mathbb R\setminus \{-1\},\star)$ is an Abelian group. b. Solve $$3\star x \star x = 15$$…