Sample solution

#include <cassert> /* needed for assert */
#include <cstddef> /* needed for std::size_t and std::ptrdiff_t */
#include <printf.hpp> /* needed for fmt::printf */

enum class StorageOrder {ColMajor, RowMajor};

struct Matrix {
   const std::size_t m; /* number of rows */
   const std::size_t n; /* number of columns */
   const std::ptrdiff_t incRow;
   const std::ptrdiff_t incCol;
   double* data;

   Matrix(std::size_t m, std::size_t n, StorageOrder order) :
         m(m), n(n),
         incRow(order == StorageOrder::ColMajor? 1: n),
         incCol(order == StorageOrder::RowMajor? 1: m),
         data(new double[m*n]) {
   }

   const double& operator()(std::size_t i, std::size_t j) const {
      assert(i < m && j < n);
      return data[i*incRow + j*incCol];
   }
   
   double& operator()(std::size_t i, std::size_t j) {
      assert(i < m && j < n);
      return data[i*incRow + j*incCol];
   }

   void init() {
      for (std::size_t i = 0; i < m; ++i) {
         for (std::size_t j = 0; j < n; ++j) {
            data[i*incRow + j*incCol] = j * m + i + 1;
         }
      }
   }

   void print() {
      for (std::size_t i = 0; i < m; ++i) {
         fmt::printf("  ");
         for (std::size_t j = 0; j < n; ++j) {
            fmt::printf(" %4.1lf", data[i*incRow + j*incCol]);
         }
         fmt::printf("\n");
      }
   }
};

void copy_matrix(const Matrix& A, Matrix& B) {
   /* copy A to B */
   assert(A.m == B.m && A.n == B.n);
   for (std::size_t i = 0; i < A.m; ++i) {
      for (std::size_t j = 0; j < A.n; ++j) {
         B(i, j) = A(i, j);
      }
   }
}

int main() {
   Matrix A(7, 8, StorageOrder::ColMajor);
   A.init();
   fmt::printf("A =\n"); A.print();
   Matrix B(7, 8, StorageOrder::RowMajor);
   copy_matrix(A, B);
   fmt::printf("B =\n"); B.print();
   delete[] A.data;
   delete[] B.data;
}
theon$ g++ -std=gnu++11 -o matrix_class6 matrix_class6.cpp
theon$ ./matrix_class6
A =
    1.0  8.0 15.0 22.0 29.0 36.0 43.0 50.0
    2.0  9.0 16.0 23.0 30.0 37.0 44.0 51.0
    3.0 10.0 17.0 24.0 31.0 38.0 45.0 52.0
    4.0 11.0 18.0 25.0 32.0 39.0 46.0 53.0
    5.0 12.0 19.0 26.0 33.0 40.0 47.0 54.0
    6.0 13.0 20.0 27.0 34.0 41.0 48.0 55.0
    7.0 14.0 21.0 28.0 35.0 42.0 49.0 56.0
B =
    1.0  8.0 15.0 22.0 29.0 36.0 43.0 50.0
    2.0  9.0 16.0 23.0 30.0 37.0 44.0 51.0
    3.0 10.0 17.0 24.0 31.0 38.0 45.0 52.0
    4.0 11.0 18.0 25.0 32.0 39.0 46.0 53.0
    5.0 12.0 19.0 26.0 33.0 40.0 47.0 54.0
    6.0 13.0 20.0 27.0 34.0 41.0 48.0 55.0
    7.0 14.0 21.0 28.0 35.0 42.0 49.0 56.0
theon$