Matrix Meaning

When considering the matrices in two dimensions, you could consider the algebraic form of the matrices or what happens geometrically.  In two dimensions all rotations are around the origin.  When considering reflections it is helpful is you don't restrict yourself to reflections in the $x$ and $y$ axes.  To show that something is sometimes true and sometimes not true it is enough to show that there is one case where the statement is true, and one case where it isn't!  You can sketch a diagram of a particular example to help show when something might, or might not, be true.

When thinking about rotations in three dimensions it may help to take an object and try turning it around different axes in different orders (make sure it isn't completely symmetrical - a ball wouldn't be of much use!). What happens? How does this relate to what you've been asked to do?

In some cases you might be able to use your examples from the two dimensional cases in the three dimensional cases as well.