4 Suppose that $A \in M{n \times k}(\mathbb{R})$ and $B \in M{m \times \ell}(\mathbb{R})$. Let $T: M{k \times m}(\mathbb{R}) \to M{n \times \ell}(\mathbb{R})$ be defined by $T(X) = AXB$.

a. (5) Show that \( T \) is a linear transformation.