Cancellation Laws

Theorem
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


 * $a b = a c \implies b = c$

That is, the group operation is cancellable.

Let $e$ be the identity element of $G$.

Then: