"It's totally right what you say, Trix,
That in a diagonal matrix
You'll find," Al confirms,
Are all zero. Now bug off and play, Trix!"
Bob Egg, The Omnificent English Dictionary in Limerick Form
The purpose of this chapter is to introduce you to matrix algebra, which has many applications. You are already familiar with several algebras: elementary algebra, the algebra of logic, the algebra of sets. We hope that as you studied the algebra of logic and the algebra of sets, you compared them with elementary algebra and noted that the basic laws of each are similar. We will see that matrix algebra is also similar. As in previous discussions, we begin by defining the objects in question and the basic operations.