# CHAPTER 15 — Product of Two Matrices

This chapter discusses the product of
two matrices.
This is an extension of the
ideas of the previous chapter.

#### Chapter Topics:

- When matrices can be multiplied together
- Result is a matrix
- Each element of the result is a dot product
- Associative property
- Not commutative
- Distributive over addition
- Multiplication with the zero matrix

Matrix-matrix products are used in computer
graphics to create the transformation matrices
that operate on points and vectors.
In a "first person game" such as DOOM the
landscape is modeled with points and vectors.
The constantly changing view you see
as the hero moves
through the landscape is created by transforming
those points and vectors.

### QUESTION 1:

Do you think it possible to multiply the following two matrices?
**A**_{4×3} **B**_{3×5}

(Make a guess, based on what you know about multiplying
a matrix with a column matrix.)