Math Is Fun Forum

I stop here because I don't know how to show the inverse must be in the intersection of H1 and H2.

And anoher question , show that the union of H1 and H2 is not a group , I think I need to use contradiction right?

I want to make a paper of summary of definitions and theorems and print it .Which software should I use , (besides Microsoft office, cuz it's just crashed)
     and second , How do u guys manage to conquer Topology , I can barely understand the proof for theorem , not to talk about applying them.

I don't quite understand what is Row-Reduced Echelon Matrices .  I know what Row-Reduced means , and I've already read the definition of Row-Reduced Echelon Matrices , but my english won't allow me to have a full understanding of what  it is.  An example will be great appreciated.

We can use a true Statement to push forward and get a new theorem or so, but how can we prove the very first of theorems? and also , if a,b,c are statements , a--> b -->c -->a, if these statements form a circle themselves , how can we determine whether they are valid?