Showing a subset does not form a subgroup (explaination wanted)
If not sure how to show that a subset does not form a subgroup. Here is the example:
Let . Show that the subset S of G defined by
of symmetric 2x2 matrices deos not form a subgroup of G.
I'm not sure where to start. I understand the three conditions:
i)ab is an element of S
ii) e is an element of S
iii)a^-1 is an element of S
But i'm not used to physically working with matrices to prove these. How do I show that at least one of these is not satisfied for S?