For $A \in M _ { 3 } ( \mathbb { C } )$, let $W _ { A } = \left\{ B \in M _ { 3 } ( \mathbb { C } ) \mid A B = B A \right\}$. Which of the following is/are true? (A) For all diagonal $A \in M _ { 3 } ( \mathbb { C } )$, $W _ { A }$ is a linear subspace of $M _ { 3 } ( \mathbb { C } )$ with $\operatorname { dim } _ { \mathbb { C } } W _ { A } \geq 3$. (B) For all $A \in M _ { 3 } ( \mathbb { C } ) , W _ { A }$ is a linear subspace of $M _ { 3 } ( \mathbb { C } )$ with $\operatorname { dim } _ { \mathbb { C } } W _ { A } > 3$. (C) There exists $A \in M _ { 3 } ( \mathbb { C } )$ such that $W _ { A }$ is a linear subspace of $M _ { 3 } ( \mathbb { C } )$ with $\operatorname { dim } _ { \mathbb { C } } W _ { A } = 3$. (D) If $A \in M _ { 3 } ( \mathbb { C } )$ is diagonalizable, then every element of $W _ { A }$ is diagonalizable.
For $A \in M _ { 3 } ( \mathbb { C } )$, let $W _ { A } = \left\{ B \in M _ { 3 } ( \mathbb { C } ) \mid A B = B A \right\}$. Which of the following is/are true?\\
(A) For all diagonal $A \in M _ { 3 } ( \mathbb { C } )$, $W _ { A }$ is a linear subspace of $M _ { 3 } ( \mathbb { C } )$ with $\operatorname { dim } _ { \mathbb { C } } W _ { A } \geq 3$.\\
(B) For all $A \in M _ { 3 } ( \mathbb { C } ) , W _ { A }$ is a linear subspace of $M _ { 3 } ( \mathbb { C } )$ with $\operatorname { dim } _ { \mathbb { C } } W _ { A } > 3$.\\
(C) There exists $A \in M _ { 3 } ( \mathbb { C } )$ such that $W _ { A }$ is a linear subspace of $M _ { 3 } ( \mathbb { C } )$ with $\operatorname { dim } _ { \mathbb { C } } W _ { A } = 3$.\\
(D) If $A \in M _ { 3 } ( \mathbb { C } )$ is diagonalizable, then every element of $W _ { A }$ is diagonalizable.