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.