How to calculate the inverse of a matrix such that it is integer and non-negative?

Question

Mathematics

In general, according to the Hill cryptosystem, for decryption, you need to calculate the inverse key matrix, but not a simple one, but a golden integer and non-negative .
It turned out to find an integer, but negative. And it becomes negative due to the fact that we make a matrix of algebraic additions from the original.
Example:
|3 3| - initial matrix A
|2 5|
|5 2| - matrix of minors M
|3 3|
|5 -2| - matrix of algebraic additions M'
|-3 3|
|5 -3| - transposed matrix ( M' )^t
|-2 3|
m = 34 (alphabet)
det = 3*5 - 3*2 = 9
det^-1 (inverse determinant) such that: det * det^-1 mod m = 1
9 * 19 mod 34 = 1
det^-1 = 19
A^-1= det^-1 * ( M' )^t mod m
It turns out:
|27 -23|
| -4 23|
It works only on a part of bigrams, that is, every other time. It needs to be somehow converted to non-negative. Tell me how this can be done.

Answer 1

It was just necessary to add the negative numbers to the size of the alphabet:
|27 -23+34|
| -4+34 23|
It turns
out |27 11|
| 30 23|

Answer 2

Add the second row to the first, and then the first to the second, and you have a positive matrix.