- #1
xago
- 60
- 0
Homework Statement
According to wikipedia, one of the requirements of group is:
For all a, b in G, the result of the operation, a • b, is also in G.
So say we have 2 (2x2) matricies as elements of a group:
[itex]\frac{0|1}{1|0}[/itex] and [itex]\frac{w|0}{0|w^{2}}[/itex]
and the product [itex]\frac{0|1}{1|0}[/itex] • [itex]\frac{w|0}{0|w^{2}}[/itex] is [itex]\frac{0|w^{2}}{w|0}[/itex]
does this mean that the matrix [itex]\frac{0|w^{2}}{w|0}[/itex] also has to be an element of that group or does it mean that the elements of the matrix itself (0,w,[itex]w^{2}[/itex]) have to just generally exist?