Minors will not be changing.

Check documentation for the function in question. (As a general rule, one should do that before posting.) The Details section explains what it does and in particular the ordering of the result.

Here is the example at hand (which should be in the body of the main message, not posted in a response). The code to get the different ordering is what is shown in the Details of the reference guide page.

mat3 = Array[a, {3, 3}];
Minors[mat3]
Reverse[Minors[mat3], {1, 2}]


(* Out[142]= {{-a[1, 2] a[2, 1] + a[1, 1] a[2, 2], -a[1, 3] a[2, 1] + 
   a[1, 1] a[2, 3], -a[1, 3] a[2, 2] + 
   a[1, 2] a[2, 3]}, {-a[1, 2] a[3, 1] + 
   a[1, 1] a[3, 2], -a[1, 3] a[3, 1] + 
   a[1, 1] a[3, 3], -a[1, 3] a[3, 2] + 
   a[1, 2] a[3, 3]}, {-a[2, 2] a[3, 1] + 
   a[2, 1] a[3, 2], -a[2, 3] a[3, 1] + 
   a[2, 1] a[3, 3], -a[2, 3] a[3, 2] + a[2, 2] a[3, 3]}}

Out[143]= {{-a[2, 3] a[3, 2] + a[2, 2] a[3, 3], -a[2, 3] a[3, 1] + 
   a[2, 1] a[3, 3], -a[2, 2] a[3, 1] + 
   a[2, 1] a[3, 2]}, {-a[1, 3] a[3, 2] + 
   a[1, 2] a[3, 3], -a[1, 3] a[3, 1] + 
   a[1, 1] a[3, 3], -a[1, 2] a[3, 1] + 
   a[1, 1] a[3, 2]}, {-a[1, 3] a[2, 2] + 
   a[1, 2] a[2, 3], -a[1, 3] a[2, 1] + 
   a[1, 1] a[2, 3], -a[1, 2] a[2, 1] + a[1, 1] a[2, 2]}} *)

Regarding the ordering, it is lexicographic based on rows and columns retained in constructing the given minor.

Welcome to Wolfram Community! Please make sure you know the rules: https://wolfr.am/READ-1ST

The rules explain how to format your code properly. Posting code Images doesn't help other members to copy your code. Please EDIT your post and make sure code blocks start on a new paragraph and look framed and colored like this.

int = Integrate[1/(x^3 - 1), x];
Map[Framed, int, Infinity]

You can also embed notebook or attach notebook.