< Matrizen < 2x2 < Dritteldrehung < Gruppe
Zeige, dass die drei reellen Matrizen
(
1
0
0
1
)
,
(
−
1
2
−
3
2
3
2
−
1
2
)
,
(
−
1
2
3
2
−
3
2
−
1
2
)
{\displaystyle {\begin{pmatrix}1&0\\0&1\end{pmatrix}},\,{\begin{pmatrix}-{\frac {1}{2}}&-{\frac {\sqrt {3}}{2}}\\{\frac {\sqrt {3}}{2}}&-{\frac {1}{2}}\end{pmatrix}},\,{\begin{pmatrix}-{\frac {1}{2}}&{\frac {\sqrt {3}}{2}}\\-{\frac {\sqrt {3}}{2}}&-{\frac {1}{2}}\end{pmatrix}}}
bezüglich der
Matrizenmultiplikation
eine
Gruppe
bilden.
Zur Lösung
,
Alternative Lösung erstellen
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