http://img145.imageshack.us/img145/9528/matrixex6.jpg 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.