Understanding Symmetric Matrix Properties: A Puzzling Example

[dirk_mec1]

Homework Statement

http://img266.imageshack.us/img266/152/78148531ur5.png

Homework Equations

A is symmetric.

The Attempt at a Solution

First of all if you calculate r^T you'll get q^TA so why it the order reversed in the picture above? Moreover I don't see why it is zero.

 

[quantumdude]

Can you go into more detail as to what those symbols mean? The superscripted T's clearly indicate that some of them are matrices, but are they all matrices? If so, then are they all square? If not, then how many rows and columns does each have?