# Subgroups and matrix homework

http://img145.imageshack.us/img145/9528/matrixex6.jpg [Broken]

I have 3 subgroup criterion.

For the first i have to show H is non empty, well here the matrix

2 1
5 3

is an element of H, so it is none empty.

The second I have to show that H is closed under the binary operation of GL2R. How do I do this? By definition ig g, h are elements of H, then gh is an element of H. I have no idea how to show this is true for it?

I can find another matrix that would be in the group of H, and I can show the product of the matrices is 1, but do I have to prove it? And how?

Thirdly I have to show the inverse of each element of H belongs to H, which is easy.

Last edited by a moderator:

I think the fastest way might be to exploit that theorem that says that if it's a subset (which it is) that has the property that $a,b \in H \Rightarrow ab^{-1} \in H$ then H is a subgroup. I say that because just exploiting the fact that the determinant is a homomorphism, it's not hard to show that ab^{-1} is in H without doing alot of math.