Let $G$ be a closed subgroup of $GL(n, \mathbb{R})$. How do I show that Lie algebra $\mathfrak{g}$ of $G$ is given by $$\mathfrak{g} = \{ B \in \mathfrak{gl}(n, \mathbb{R}) : \forall t \in \mathbb{R}, e^{tB} \in G \} $$
$\mathfrak{gl}(n, \mathbb{R})$ is the Lie algebra of $GL(n,\mathbb{R})$.