Klein-4 group

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Definition

The Klein-4 group (AKA: Viergruppe), $V_4=\{1,a,b,c\}$ is a group on 4 elements with the operation $*:V_4\times V_4\rightarrow V_4$ defined as follows:

$\begin{array}{|c|cccc|} \hline V_4 & 1 & a & b & c \\\hline 1 & 1 & a & b & c \\ a & a & 1 & c & b \\ b & b & c & 1 & a \\ c & c & b & a & a \\\hline \end{array}$
Operator tables for the Klien-4 group

Recall that to calculate the product say, $a*b$ we look at the row corresponding to $a$ and find the entry in the $b$ column, which is $c$ here (the same as $b*a$, so be sure you're doing it the correct way)

Claim: this is indeed a group.