You can't use HTML tagsinsideLaTex. Use [ math ]G= GL_2(\bold{R})[ /math ] (without the spaces) to get .

use "[ math ]\begin{bmatrix}a & b \\ c & d\end{bmatrix}[ math ]" to get " "Show that the subset S of G defined by

As for (ii), the identity is wjhichof 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?isa symmetric matrix.

As for (iii), the inverse of . a "general" symmetric matrix, can be shown to be , also a symmetric matrix.

So I recommend you focus on (i). Is the product of two symmetric matrices symmetric? What is ?