$$A B = A C L C$$
$\left\{\begin{matrix}\\A=0\text{, }&\text{unconditionally}\\A\in \mathrm{R}\text{, }&B=LC^{2}\end{matrix}\right.$
$$AB=AC^{2}L$$
$$AB-AC^{2}L=0$$
$$AB-ALC^{2}=0$$
$$\left(B-LC^{2}\right)A=0$$
$$A=0$$
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$\left\{\begin{matrix}\\B=LC^{2}\text{, }&\text{unconditionally}\\B\in \mathrm{R}\text{, }&A=0\end{matrix}\right.$
$$AB=ALC^{2}$$
$$\frac{AB}{A}=\frac{ALC^{2}}{A}$$
$$B=\frac{ALC^{2}}{A}$$
$$B=LC^{2}$$