can someone help me understand how you go from (2) to (3) on this web page... and also (4) (5) (6)
Here yah go champ, this should take care of the confusion from (2)->(3) for you:
Matrix multiplication - Wikipedia, the free encyclopedia
And then it looks like (3) (4) and (5) are just rules for the elements of the resulting left side matrix elements on the bottom left, diagonal, and upper right, respectively. Hope that helps.