If $A=\begin{pmatrix}a&b\\c&d\end{pmatrix}$ where $a,b,c,d \in R$ such that $AB=BA$ for each $2\times 2$ matrix $B$,then $b^2+c^2$

Question

$\begin{array}{1 1}\text{can have any positive value}\\0\\1\\2\end{array} $