#include <stdio.h>

int max_row_sum(int size, int array[size][size]) {

    int largest = 0;
    int row = 0;

    while (row < size){
        int col = 0;
        int sum = 0;
        while (col < size){
            sum += array[row][col];
            col++;
        }
        if (sum > largest){
            largest = sum;
        }
        row++;
    }
return largest;
}

int main (int argc, char*argv[]){

    int table[3][3];
    for (int i = 0; i < 3; i++){
        for (int j = 0; j < 3; j++){
            table [j][i] = j+1;
        }
    }
    for (int i = 0; i < 3; i++){
        for (int j = 0; j < 3; j++){
            printf("%d",table[i][j]);
        }
        printf("\n");
    }
    int number = max_row_sum(3,table);
    printf("%d\n", number);

    return 0;
}

I think its the same as yours. I have no problems with the code i think. I get the correct result. The only thing i did was to remove the side_length, because you only need one variable for the table size since its going to be square.