If not sure how to show that a subset does not form a subgroup. Here is the example:

Let $\displaystyle G=GL_2(R)$. Show that the subset S of G defined by

$\displaystyle

S={[

a b

c d

]|b=c}

$

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?