I don't know how to prove the following and need help.

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> Let $M\_{n\times n}$ be the vector space of matrices over $\mathbb{C}$. Let $A\in M\_{n\times n}$ be fixed matrices, and $X\in M\_{n\times n}$ be variable matrix. Define the linear transformation $T$ on $M\_{n\times n}$ by $T(X)=AX-XA$. Prove that the range of $T$ is at most $n^2-n$.
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My idea is to use Kronecker Product to convert $AX-XA$ to a vector form equation like $\overline{A}{y}$ but got stuck on how to proceed.