how does matrix division work in matlab?

you can't divise a matrix by a matrix

[Torsten]

You see how it works ? It's element-by-element division.

A = [4 16 ; 36 64];
B = [2 4 ; 6 8];
A./B

ans = 2×2

2 4 6 8

[Voss]

rdivide, ./, mrdivide, /, ldivide, .\, mldivide, \

Answer 1

[Walter Roberson]

Mathematically (but not in practice) if you have a column vector b and a square array A, then A*x = b is the same as saying that inv(A)*A*x = inv(A)*b but inv(A)*A is the identity matrix so you get to x = inv(A)*b

For non-square matrices A, instead of inv(A) you would use pinv(A)*b where pinv(A) is Moore-Penrose pseudo-inverse pinv

This is not what is actually computed. See https://www.mathworks.com/help/matlab/ref/mldivide.html#bt4jslc-6 for a flow-chart of the algorithms used.