在2D数组中通过重载数组下标操作符进行访问

对于下面表示矩阵的函数

class m // matrix
{
    private:
        double **matrix;
        int nrows, ncols;

        class p
        {
            private:
                double *arr;
            public:
                p (double *a)
                    :   arr (a)
                {
                }
                double &operator[] (int c)
                {
                    return arr[c];
                }
        };

    public:
        m (int nrows, int ncols)
        {
            this->matrix = new double *[nrows];
            for (int i = 0; i < nrows; ++i)
            {
                this->matrix[i] = new double [ncols];
            }
            this->nrows = nrows;
            this->ncols = ncols;
        }
        ~m()
        {
            for (int i = 0; i < this->nrows; ++i)
            {
                delete [] this->matrix[i];
            }
            delete this->matrix;
        }
        void assign (int r, int c, double v)
        {
            this->matrix[r][c] = v;
        }

        p operator[] (int r)
        {
            return p (this->matrix[r]);
        }
};

操作符用于元素访问，但不能用于元素更改。如何将assign()函数的功能添加到算子中?