Let G = GL(2, R) be the group of all 2 × 2 matrices with real entries and a nonzero determinant.

Let H = SL(2, R) be the set of all 2 × 2 matrices with real elements and determinant equal to 1.

Test it

a) H is a normal subgroup in G.

b) G/H is isomorphic to the multiplicative group of reals * , · >

Answer rating: 100% (QA)

a To show that H is a normal subgroup in G we need to prove that for every g in G and h in H the pro... View the full answer