C++ Trying to find the minimum element of 2D vector with lambda

I'm currently trying to find the minimum element of a 2D vector. I'm trying to practice using C++11 lambda functions and figured this might be good practice, but can't seem to get it compiling.

I'm aware that I could do the following:

vector<vector<int>> matrix = {
                                {1, 2, 3, 4, 5 },
                                {6, 7, 8, 9, 10 },
                                {5, 6, 8, 1, 12 },
                                {1, 7, 2, 4, 18 },
};

int result = std::numeric_limits<int>::max();
for(const auto& row : matrix)
{
  int minElemInRow = *std::min_element(row.begin(), row.end());
  result = std::min(result , minElemInRow);
}
return result;

but was wondering if the same could be done with a lambda function. Currently, this is my best attempt:

vector<vector<int>> matrix = {
                                {1, 2, 3, 4, 5 },
                                {6, 7, 8, 9, 10 },
                                {5, 6, 8, 1, 12 },
                                {1, 7, 2, 4, 18 },
};

return *std::min_element(matrix.begin(), matrix.end(), 
  [](const auto& row)
  {
    return *std::min_element(row.begin(), row.end());
  });

I get the error: error C2672: 'operator __surrogate_func': no matching overloaded function found

How I feel it should be working is that the outer min_element will pass in a row at a time (which is just a reference to a vector), from which I can return the smallest, which will then be compared against other rows.

I thought that the problem might be that the lambda would be receiving an iterator to a vector of ints rather than a reference to the vector of ints, but dereferencing doesn't seem to be helping.

Is there a better way to be doing what I'm trying to do?