Hi, if someone can explain how to get the answer to this is would be greatly appreciated.

Let:

G be the set of matrices of the form:

[a b : 0 1]

H be the set of matrices of the form:

[a 0 : 0 1]

K be the set of matrices of the form:

[1 b : 0 1]

Q1: Is G isomorphic to H x K? Prove it, or give a counterexample.

Q2: Is G/K isomorphic to H? Prove it, or give a counterexample.

Any help would be nice.

Thanks