# Thread: Let G and H be the following subgroups of GL(2; R):

1. ## Let G and H be the following subgroups of GL(2; R):

Let G and H be the following subgroups of GL(2, R):
G ={ [a b,0 1 ] | a and b are in R and a is not equal to 0} and H={ [ 1 b ,0 1 ] | b is in R}

:
(a) Prove that H is normal in G.
(b) Use the First Isomorphism Theorem to prove that G=H is isomorphic to R the
group of nonzero real numbers under multiplication.

2. ## Re: Let G and H be the following subgroups of GL(2; R):

Hi,
I hope maybe by now you have been able to prove the result. However, here is a solution with just a couple of details omitted: