If $A=\begin{bmatrix} 1 & 2\\3 & 4\end{bmatrix}, B=\begin{bmatrix}a & 0\\0 & b \end{bmatrix}; a, b \in N, $ then
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → There exist infinite B, when AB = BA
$AB=BA$
$\begin{bmatrix} 1 & 2\\3 & 4\end{bmatrix}\begin{bmatrix}a & 0\\0 & b \end{bmatrix}=\begin{bmatrix}a & 0\\0 & b \end{bmatrix}\begin{bmatrix} 1 & 2\\3 & 4\end{bmatrix}$
$\begin{bmatrix} a & 2b\\3a & 4b\end{bmatrix}=\begin{bmatrix} a & 2b\\3a & 4b\end{bmatrix}$
$⇒a=b$
Infinite number of B when AB = BA