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Let \( A=\left(\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right) \) and \( B=\left(\begin{array}{ll}a & 0 \\ 0 & b\end{array}\right), a, b \in N \). Then
\( \mathrm{P} \)
(1) There cannot exist any \( B \) such that \( A B=B A \)
(2) There exist more than one but finite number of \( B \) 's such that \( A B=B A \)
(3) There exists exactly one \( \mathrm{B} \) such that \( A B=B A \)
(4) There exists infinitely many \( B \) 's such that \( A B=B A \)
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