### Introduction

When we wish to multiply matrices together we have to ensure that the operation is possible - and this is not always so. Also, unlike number arithmetic and algebra, even when the product exists the order of multiplication may have an effect on the result. In this Section we pick our way through the minefield of matrix multiplication.

#### Prerequisites

- understand the concept of a matrix and associated terms.

#### Learning Outcomes

- decide when the product $AB$ exists
- recognise that $AB\ne BA$ in most cases
- carry out the multiplication $AB$
- explain what is meant by the identity matrix $I$

#### Contents

1 Multiplying row matrices and column matrices together2 Multiplying two 2 by 2 matrices

3 Some surprising results

4 Multiplying two 3 $\times $ 3 matrices

5 Multiplying non-square matrices together

6 The rules of matrix multiplication

6.1 Application of matrices to networks

7 Engineering Example 1

7.1 Communication network