Show that $(\mathbb{Q}\setminus\{0\}, *)$ is a subgroup of $(\mathbb{R}\setminus\{0\}, *)$

Question

I know I have to show

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1) $1\in\mathbb{Q}$

2) $a,b\in\mathbb{Q}$ implies $a*b\in\mathbb{Q}$

3) $a\in\mathbb{Q}$ implies $a^{-1}\in\mathbb{Q}$

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but I don't know how go about it. Can anyone give some hints or a place to start?