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2. Show that if [tex]a \in \textbf{Q}[/tex] and [tex]t \in \textbf{Q}[/tex], then [tex]a + t \in \textbf{I}[/tex] and [tex]at \in \textbg{I}[/tex] as long as [tex]a \neq 0[/tex].

I'm just a little shady on showing these properties, so if someone could give me a little reminder, that would be swell. It's been a few years since I've taken an Algebra course.