Subgroups of the general linear group

Below are three subgroups of ${\mathrm{GL}}_n(\mathbb{R})$, the group of invertible $n\times n$ matrices with real entries.

${\mathrm{SL}}_n(\mathbb{R})$

The subset of ${\mathrm{GL}}_n(\mathbb{R})$ consisting of [what matricies?]. "S" is short for "special".

${\mathrm{O}}_n(\mathbb{R})$

The subset of ${\mathrm{GL}}_n(\mathbb{R})$ consisting of [what matricies?]. "O" here is short for "orthogonal".

${\mathrm{SO}}_n(\mathbb{R})$

The subset of ${\mathrm{O}}_n(\mathbb{R})$ consisting of [what matricies?].

Can you proof that these 3 subsets form subgroups?