Hi, I think I have this correct but I need someone to confirm my working.

Let G be the set of matrices of the form:

[a b]

[0 1]

for $\displaystyle a,b \in \mathbb{R}$

Prove that G is a subgroup of GL2(R).

1. if $\displaystyle x,y \in G$, then $\displaystyle xy \in G$

Let x=[a b : 0 1] and y =[c d : 0 1]

Then

xy=[ac ad+b : 0 1]

$\displaystyle \implies xy \in G$

2. If a=1, b=0, then I = [1 0 : 0 1]

$\displaystyle \implies I \in G$

3. if $\displaystyle x \in G$, then $\displaystyle x^{-1} \in G$.

x=[a b : 0 1], then x^{-1} = [1 -b : 0 a]

thus, $\displaystyle x^{-1} \in G$.

Thus, G is a subgroup of GL2(R).

Thanks