Question: For every matrix A M_n(F), let C(A) = {X M_n(F) | AX = XA} denote the centralizer of A. (a) Please show that C(A) is

For every matrix A M_n(F), let C(A) = {X M_n(F) | AX = XA} denote the centralizer of A. (a) Please show that C(A) is a subspace of M_n(F). (b) Please determine C(e_11) and compute its dimension (for arbitrary n).

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