Group Product/Examples/a x b = c

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Examples of Operations on Product Elements

Solve for $x$ in:

$a x b = c$


\(\ds a x b\) \(=\) \(\ds c\)
\(\ds \leadsto \ \ \) \(\ds a^{-1} a x b\) \(=\) \(\ds a^{-1} c\) Product of both sides with $a^{-1}$
\(\ds \leadsto \ \ \) \(\ds a^{-1} a x b b^{-1}\) \(=\) \(\ds a^{-1} c b^{-1}\) Product of both sides with $b^{-1}$
\(\ds \leadsto \ \ \) \(\ds x\) \(=\) \(\ds a^{-1} c b^{-1}\) Group Axiom $\text G 3$: Existence of Inverse Element