  Let $\mu$ be a probability measure on $\text{GL}_d(\mathbb{R})$ and denote by
$S_n:= g_n \cdots g_1$ the associated random matrix product, where $g_j$ are
i.i.d. with law $\mu$. Under the assumptions that $\mu$ has a finite
exponential moment and generates a proximal and strongly irreducible semigroup,
we prove a Berry-Esseen bound with the optimal rate $O(1/\sqrt n)$ and a
general Local Limit Theorem for the coefficients of $S_n$.
