World Matrix

The reason we use matrix cuz one is translaton, and other one is,in game or graphic, we usually using 'World Matrix' to represnet [Translation] x [Rotation] x [Scale].

The order is Matter!, We will start from Scale, Rotation and the last is Translation.

You will see the Translation Matrix is identity matrix combine with tx,ty,tz.

Why translation special?

Matrix Translation is not linear translation.

Further read:

https://math.libretexts.org/Bookshelves/Linear_Algebra/Fundamentals_of_Matrix_Algebra_(Hartman)/05%3A_Graphical_Explorations_of_Vectors/5.02%3A_Properties_of_Linear_Transformations#5below

Think about shear technique that we raise up the dimension, 2D -> 3D. And the result of shear in 3D is a translation in the 2D plane.

It is work with any dimension.

So that is one of the reason why we have to get 4 dimention matrix in 3D.