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If $A=\begin{bmatrix} 1 & 2\\3 & 4\end{bmatrix}, B=\begin{bmatrix}a & 0\\0 & b \end{bmatrix}; a, b \in N, $ then |
There can't exist any B such that AB =BA There exist more than one B, but finite in number when AB = BA There exists exactly one B, when AB =BA There exist infinite B, when AB =BA |
There exist infinite B, when AB =BA |
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 |
