JEE Math Practice Question

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

1. A.there cannot exist any $$B$$ such that $$AB=BA$$
2. B.there exist more then one but finite number of $$B'$$s such that $$AB=BA$$
3. C.there exists exactly one $$B$$ such that $$AB=BA$$
4. D.there exist infinitely many $$B'$$s such that $$AB=BA$$