question_answer

Let \[A=\left[ \begin{matrix}    1 & 2  \\    3 & 4  \\ \end{matrix} \right]\] and \[B=\left[ \begin{matrix}    a & 0  \\    0 & b  \\ \end{matrix} \right];\] \[a,\]\[b\in N\]  Then, ________.

A)  There exists more than one but finite number of B's such that AB = BA

B)  There cannot exist any B such that AB = BA

C)  There exist infinitely many B's such that AB = BA

D)  There exists exactly one B such that AB = BA

E)  None of these