Does the Matrix \(\frac{0|w^{2}}{w|0}\) Have to Be an Element of the Group?

[xago]

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:
$\frac{0|1}{1|0}$ and $\frac{w|0}{0|w^{2}}$
and the product $\frac{0|1}{1|0}$ • $\frac{w|0}{0|w^{2}}$ is $\frac{0|w^{2}}{w|0}$

does this mean that the matrix $\frac{0|w^{2}}{w|0}$ also has to be an element of that group or does it mean that the elements of the matrix itself (0,w,$w^{2}$) have to just generally exist?

 

[Dick]

"the result of the operation, a • b, is also in G" is pretty unambiguous. It has to be an element of the group.

 

[tiny-tim]

hi xago!

does this mean that the matrix $\frac{0|w^{2}}{w|0}$ also has to be an element of that group …

yes