Question

8. Let G = GL2(R). (Tables are actually matrices)

(a) Prove that T = {

a	0
c	d

}| a, c, d ∈ R, ad ≠ 0) is a subgroup of G.

(b) Prove that D = {

a	0
0	d

} | a, d ∈ R, ad ≠ 0) is a subgroup of G.

(c) Prove that S = {

a	b
c	d

} | a, b, c, d ∈ R, b = c ) is not a subgroup of G.

(d) Determine whether A = {

a	b
0	0

} | a, b ∈ R ) is a subgroup of G.

(e) Determine whether B = {

0	b
c	0

} | b, c ∈ R ) is a subgroup of G.

(f) Determine whether C = {

1	0
0	d

} | d ∈ R, d ≠ 0) is a subgroup of G.

Answer 1