Cube symmetry/Examples/Action on vertices/Exercise

Suppose that the vertices $(\pm 1,\pm 1,\pm 1)$ of a cube are denoted by $1,2,3,\dots ,8$. Determine the value tables that describe the permutations of the vertices induced by the following (proper or improper) symmetries of the cube:

a) $\left(\begin{array}{ccc}1& 0& 0\\ 0& 0& 1\\ 0& -1& 0\end{array}\right)$,

b) $\left(\begin{array}{ccc}-1& 0& 0\\ 0& 0& -1\\ 0& -1& 0\end{array}\right)$,

c) $\left(\begin{array}{ccc}0& 0& 1\\ 0& 1& 0\\ -1& 0& 0\end{array}\right)$.

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