Let G be the set of matrices over R.
Show that G is isomorphic to .
I know GL2R represents the matrices
1 0
0 1
-1 0
0 1
1 0
0 -1
-1 0
0 -1
But how can I show it is isomorphic to ?
Something doesn't fit in here: if R is the real numbers, then denotes the group of all invertible 2 x 2 matrices with real entries and this is an infinite group, so it cannot possibly be isomorphic with the Klein group, a group of order 4.
Please do detail what you mean by
Tonio
Looks like i've made a mistake in the translation of the question. I misused notation.
The questions direct translation is:
Let G be the following set of matrices over R:
1 0
0 1
-1 0
0 1
1 0
0 -1
-1 0
0 -1
Show that G is isomorphic to Z_2 x Z_2.
This makes more sense, right?