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# Let $C=\begin{bmatrix}C_{11}&C_{12}\\C_{21}&C_{22}\end{bmatrix}$ be a $2\times 2$ matrix and there exist $2\times 2$ matrices $A$ and $B$ such that $C=AB-BA$ then

$\begin{array}{1 1}(A)\;C_{11}-C_{12}=0&(B)\;C_{11}+C_{22}=0\\(C)\;C_{12}+C_{21}=0&(D)\;C_{12}-C_{21}=0\end{array}$

Given :
$C=\begin{bmatrix}C_{11}&C_{12}\\C_{21}&C_{22}\end{bmatrix}$
$C=AB-BA$
$\therefore C_{11}+C_{22}=0$
Hence (B) is the correct answer.