How to show a matrix is a subgroup of a group G.

[kathrynag]

Homework Statement

Let G=GL2(R)
Show that T=matrix with row 1= a, b and row 2 = 0, d with ad\neq0 is a subgroup of G.

Homework Equations

The Attempt at a Solution

I'm sort of confused on how to show it is a subgroup.

 

[fzero]

To start out, what are the properties that a matrix must have for it to be an element of GL(2,R)? Do matrices of the form T have these properties?

What properties must a subgroup have? If T₁ and T₂ have the form stated, what about the product T₁ T₂ ?

 

[Mark44]

Homework Statement

Let G=GL2(R)
Show that T=matrix with row 1= a, b and row 2 = 0, d with ad\neq0 is a subgroup of G.

Homework Equations

The Attempt at a Solution

I'm sort of confused on how to show it is a subgroup.

Pretty much the same way you show that any set is a subgroup of the group it belongs to. I don't remember what GL2(R) means, but I suspect it consists of 2 x 2 matrices with entries in R, and the operation is probably matrix multiplication.

 

[kathrynag]

Ok I guess then I'm kinda confuses on subgroups in general

 

[Mark44]

Ok I guess then I'm kinda confuses on subgroups in general

Time to look at the definition...

 

[kathrynag]

it must be a group under the same operation on G

 

[fzero]

It would probably help you a lot to list the group axioms and verify them in the case of GL(n,R). Then you can try to verify them for the conjectured subgroup in your problem.