Let $D \in M_p(\mathbb{K})$ be a diagonal matrix. Let $(\Delta, +)$ be the additive subgroup of $M_p(\mathbb{R})$ formed by diagonal matrices. Show that $E$ defines a group morphism from $(\Delta, +)$ to $(GL_p(\mathbb{R}), \times)$.
Let $D \in M_p(\mathbb{K})$ be a diagonal matrix. Let $(\Delta, +)$ be the additive subgroup of $M_p(\mathbb{R})$ formed by diagonal matrices.
Show that $E$ defines a group morphism from $(\Delta, +)$ to $(GL_p(\mathbb{R}), \times)$.