Orthogonal Group is Subgroup of General Linear Group

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

Then $\operatorname O \left({n, k}\right)$ is a subgroup of the $n$th general linear group on $k$, $\operatorname{GL} \left({n, k}\right)$.