= Solution
{c}
For any $x$, choose $z$ with $x*z=e$. By <5/b/ii>, $z*x=e$ as well. <Associativity> and the right <identity element> property now give
$$
e*x=(x*z)*x=x*(z*x)=x*e=x.
$$
Thus $e$ is also a left <identity element>. The given <binary operation> is closed on $X$ and <associative>, $e$ is a two-sided <identity element>, and each $x$ has the two-sided <inverse element> $z$. All <group axioms> hold, so \b[$(X,*)$ is a <group>]. This is the <one-sided group axioms criterion>.
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