Class/Course - Engineering Entrance

Subject - Mathematics

Chapter - Matrices and Determinants

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Q.1 Let A = $\begin{bmatrix} 1 &2 \\ 3 &4 \end{bmatrix}$ and B = $\begin{bmatrix} a &0 \\ 0 &b \end{bmatrix}$, a, b ∈ N. Then
  there exist more than one but finite number of B's such that AB = BA
  there exist exactly one B such that AB = BA
  there exists infinitely many B's such that AB = BA
  there cannot exist any B such that AB = BA