We identify $M_3(\mathbb{R})$ with the linear endomorphisms of $V$. Let $G$ be the set of endomorphisms $g$ such that $$B(gu,gv) = B(u,v)$$ for all $u,v\in V$. Show that $G$ is a group under composition of linear maps.
We identify $M_3(\mathbb{R})$ with the linear endomorphisms of $V$. Let $G$ be the set of endomorphisms $g$ such that
$$B(gu,gv) = B(u,v)$$
for all $u,v\in V$.
Show that $G$ is a group under composition of linear maps.