Let $G$ be a group with neutral element $e$.

A **subgroup** $H$ of $G$ is a subset of $G$ that is **closed under group composition and under taking inverses**.

Let ${\rm GL}(n,{\mathbb R})$ be the group of real $n$ by $n$ matrices with non-zero determinant, $n\ge 1$.

It is called the *General Linear Group*.

Which of the following subsets of ${\rm GL}(n,{\mathbb R})$ are **NOT** subgroups of ${\rm GL}(n,{\mathbb R})$?

Select **ALL** that apply.