Let $A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$ and $B = \begin{bmatrix} a & 0 \\ 0 & b \end{bmatrix}$, $a, \; b,\; \in N$. Then :

Question

( A ) there exists infinitely many $B's$ such that $AB = BA$
( B ) there exists exactly one B such that $AB = BA$
( C ) there exist more than one but finite number of $B's$ such that $AB =BA$
( D ) there cannot exist any B such that $AB = BA$