vv, C++ (vc++) - rextester

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//Microsoft (R) C/C++ Optimizing Compiler Version 19.00.23506 for x64

#include <iostream>
#include <set>

struct Matrix{
    static constexpr int base = 5;
    int a[base][base];
    
    Matrix(){
        for(int line = 0; line < Matrix::base; ++line){
            for(int column = 0; column < Matrix::base; ++column){
                a[line][column] = 0;
            }
        }
    
    }
};

bool operator<(const Matrix &left, const Matrix &right){
    for(int line = 0; line < Matrix::base; ++line){
        for(int column = 0; column < Matrix::base; ++column){
            if(left.a[line][column] != right.a[line][column]){
                return left.a[line][column] < right.a[line][column];
            }
        }
    }

return false;
}

int main(){
    
    Matrix a;
    a.a[1][0] = 1;
    
    Matrix b;
    b.a[0][1] = 1;
    
    Matrix c;
    c.a[0][1] = 2;
    
    //false
    std::cout << std::boolalpha << (a < a) << std::endl;
    //true false
    std::cout << std::boolalpha << (a < b) << " " << (b < a) << std::endl;
    //true true true 
    std::cout << std::boolalpha << (a < b) << " " << (b < c) << " " << (a < c) << std::endl;
}

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Compilation time: 1,61 sec, absolute running time: 0,32 sec, absolute service time: 1,94 sec