Pointer to portions of array. Operations with filtered array

Following the question in Pointer to portions of array, a structure that does operations with portions of an array was proposed.

However, I am having a problem when calling functions that change entries in the matrices.

When defining operations for matrices it is standard to pass by reference. However, when I use the same structure for the filtered array I get:

error: cannot bind non-const lvalue reference of type ‘subMat&’ to an rvalue of type ‘subMat’

Here is the code:

#include <vector>
#include <array>
#include <iostream>

// define matrix 4x4
typedef std::array<double, 16> matrix4;

// define matrix 3x3
typedef std::array<double, 9>  matrix3;

struct subMat{

    matrix4& matrix_;

    const double& operator[](size_t index) const
    {
        static size_t mapping[] = {0, 1, 2, 4, 5, 6, 8, 9, 10};
        return matrix_[mapping[index]];
    }
    double& operator[](size_t index)
{
    static size_t mapping[] = {0, 1, 2, 4, 5, 6, 8, 9, 10};
    return matrix_[mapping[index]];
}


    subMat (matrix4& A): matrix_(A){}
};

template <typename T>
double sum_of_elements(const T& arr)
{
    double res = 0;
    for (int i=0;i <9; ++i) res += arr[i];
    return res;
}

template <typename T>
void test(T& arr)
{
    for (int i=0;i <9; ++i)
    {
        arr[i] = 1;
    } 
}


int main(int argCount, char *args[])
{
    std::vector<matrix4> myBlockMatrix(5);

    for (int i=0; i < myBlockMatrix.size(); i++)
    {
        for (int j = 0; j<myBlockMatrix[0].size(); j++)
        {
            myBlockMatrix[i][j] = i*j;
        }
    }

    for (int i = 0; i<myBlockMatrix.size(); i++)
    {
        std::cout << sum_of_elements(subMat(myBlockMatrix[i])) << std::endl; // this owrks
    }

    test(subMat(myBlockMatrix[0])); // this does not work

    subMat a = subMat(myBlockMatrix[0]); 
    test(a); // this works and changes the values in myBlockMatrix

    return 0;
}

The question is: What can I do with this structure to re-use the previous functions for matrix3. Do I need to always create a new instance of subMat to do operations? Or is there a way to use subMat(myBlockMatrix[0]) inside the function argument?