Exercise 12, § 2

Under a multiplicative law on E, let $a \in E$ be such that $\gamma_a$ is surjective. (a) Show that, if there exists $u$ such that $ua = a$, then $ux = x$ for all $x \in E$. (b) For an element $b \in E$ to be such that $ba$ is left cancellable, it is necessary and sufficient that $\gamma_a$ be surjective and that $b$ be left cancellable.