Let $M_n(\mathbb{R})$ be the real vector space of all $n \times n$ matrices with real entries, where $n \geq 2$. Let $A \in M_n(\mathbb{R})$. Consider the subspace $W$ of $M_n(\mathbb{R})$ spanned by ${I_n, A, A^2, \ldots}$. Then the dimension of $W$ over $\mathbb{R}$ is necessarily

(A) ∞.

(B) $n^2$.

(C) $n$.

(D) at most $n$.

(A) ∞.

(B) $n^2$.

(C) $n$.

(D) at most $n$.