I'm looking to prepare myself for all sorts of proofs which deal with sets of matrices as groups. Here's an example I'm having a tough time recalling how to complete.
Show that the set GL2(R) of all invertible 2x2 matrices with real
entries is a group under usual matrix multiplication. Is the group abelian?
Showing that the group is abelian will hopefully be easy once I prove the original statement. I should simply take two arbitrary matrices and multiply them, then swap them and multiply to view that I shall most likely have a different result (I don't believe matrices commute).
Thanks for any help!