Orthogonal Group is Subgroup of General Linear Group

Theorem
Let $k$ be a field.

Let $\operatorname O \left({n, k}\right)$ be the $n$th orthogonal group on $k$.

Let $\operatorname{GL} \left({n, k}\right)$ be the $n$th general linear group on $k$.

Then $\operatorname O \left({n, k}\right)$ is a subgroup of $\operatorname{GL} \left({n, k}\right)$.