題組內容

6 Let $A = \begin{bmatrix} 1 & 4 \\ 3 & 2 \end{bmatrix}$. Define $T : M_{2 \times 2}(\mathbb{R}) \to M_{2 \times 2}(\mathbb{R})$ such that $T(X) = XA - AX$.

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