How do you find the inverse of a matrix without the inv() command?

So I know the easiest way to find the inverse of a matrix is just simply using the inv() command but I wanted to know if there was a long form method. Specifically is there a way to code the rearranging of the values in a matrix?

from [a b;c d] ====> to [d -b;-c a]

Answer 1

[Matt J]

There is this File Exchange contribution:

https://www.mathworks.com/matlabcentral/fileexchange/12692-adjugate-adjoint-of-a-square-matrix?s_tid=srchtitle

Example,

>> A=[1,2;3,4]

A =

1 2

3 4

>> adjugate(A).'

ans =

4.0000 -3.0000

-2.0000 1.0000

[Connor Lance]

Exactly what I'm looking for, I appreciate it!

[Paul]

The Symbolic Math Toolbox has function that computes the adjugate. It works for doubles

A = [1 2;3 4];
adjoint(A)

ans = 2×2

4.0000 -2.0000 -3.0000 1.0000