## Learning Algebra 2

##### 24th Nov, 2021

### Matrix multiplication as composition | Chapter 4

Composition is the product of two matrices.

How to compute the product of two matrices:

These are transformations that must be applied sequentially. From previous lessons, we know that each column in a
matrix is the coordinate where î (i hat) and ĵ (j hat) will be after the transformation. So, first we must
transform the first column [e, g] of the first matrix M1, to see where î goes.

And then we do the same for the second column [f, h] of the first matrix M1, to see where ĵ will go.

And that gives us our composition!

A few properties of matrix multiplication:

- It's non-Commutative: Order maters. AB ≠ BA
- It's Associative: (AB)C = A(BC)

Done. Let's move to the 3D realm.