Cancellation Laws/Proof 3
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Corollary to Group has Latin Square Property
Let $G$ be a group.
Let $a, b, c \in G$.
Then the following hold:
- Right cancellation law
- $b a = c a \implies b = c$
- Left cancellation law
- $a b = a c \implies b = c$
Suppose $x = b a = c a$.
That is, $x = b a = c a \implies b = c$.
Similarly, suppose $x = a b = a c$.
That is, $a b = a c \implies b = c$.