Let $\displaystyle G$ be a group. Then

(a) $\displaystyle G$ has a unique identity, and

(b) each element in $\displaystyle G$ has a unique inverse.

The table below shows an abelian group with $\displaystyle 3$ elements:

$\displaystyle \begin{tabular}{lccr}

*&a&b&c\\

\cline{2-4}a&a&b&c\\

b&b&c&c\\

c&c&a&b

\end{tabular}$

I can see the identity is show on the first row and column, but I don't see the inverse of each elements. Does it mean that the inverses are not in the group?