What is the mathematical meaning of transposition and matrix multiplication?

Question

Linear algebra

Since matrices are just a way of writing equations, it is clear that you can subtract rows from each other and multiply by scalars, but what is the point of transposing and multiplying matrices

Answer 1

Matrix multiplication is actively used in computer graphics.
Let's take for example an ordinary character with x,y,z coordinates. To move this character, we multiply its coordinates by the displacement matrix. To rotate a character, we multiply it by the rotation matrix (or use quaternions).
Inverse matrices are also actively used in 3D graphics, but I don't remember what for :)
In general, a lot is done in 3D graphics through vectors, matrices and quaternions.

Answer 2

https://en.wikipedia.org/wiki/Transpose
https://math.stackexchange.com/questions/37398/wha...
https://math.stackexchange.com/questions/24456/mat...
https ://math.stackexchange.com/questions/131889/ho...

Answer 3

This is a way to solve systems of linear equations.