Solve for B
\left\{\begin{matrix}\\B=0\text{, }&\text{unconditionally}\\B\in \mathrm{R}\text{, }&G=KM\end{matrix}\right.
Solve for G
\left\{\begin{matrix}\\G=KM\text{, }&\text{unconditionally}\\G\in \mathrm{R}\text{, }&B=0\end{matrix}\right.
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1GB-MKB=0
Subtract MKB from both sides.
BG-BKM=0
Reorder the terms.
\left(G-KM\right)B=0
Combine all terms containing B.
B=0
Divide 0 by G-MK.
BG=BKM
Reorder the terms.
\frac{BG}{B}=\frac{BKM}{B}
Divide both sides by B.
G=\frac{BKM}{B}
Dividing by B undoes the multiplication by B.
G=KM
Divide MKB by B.
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