Question

$$A B = A C L C$$

Solve for A

$\left\{\begin{matrix}\\A=0\text{, }&\text{unconditionally}\\A\in \mathrm{R}\text{, }&B=LC^{2}\end{matrix}\right.$

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Solve for B

$\left\{\begin{matrix}\\B=LC^{2}\text{, }&\text{unconditionally}\\B\in \mathrm{R}\text{, }&A=0\end{matrix}\right.$

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