multiplying two arrays of different dimensions in c++ - c++

Question

for my assignment I have to multiply two matrices together to create a new one. I will then sort the new one from an inherited class. My question is what is the format to multiply two arrays of different dimensions my first one a1d is 5 integers. My other one a2d is a 5x10 array. What is the correct way to multiply these together being that they are different sizes and dimensions. Do I multiply a1d by every row of a2d? I am going to output the products to a 1 dimensional array so that sorting is easier. I have drawn out the two arrays as tables to help me visualize it. I will attach the short code I have and my illustration. This is in C++.
#pragma once
#include<ctime>
#include<iostream>
#include<cmath>
using namespace std;
class matrices
{
private:
int* a1d[5]; // Old Code:int* a1d = new int[5];
int** a2d = new int* [5];
public:
int* matrix;
matrices();
~matrices();
int* filla1d();
int* filla2d();
int* multiply();
};
int* matrices::filla1d() {
for (int i = 0; i < 5; i++) {
a1d[i] = new int;
}
for (int i = 0; i < 5; i++) {
*a1d[i] = rand() % 10 + 1;
}
return *a1d;
}
int* matrices::filla2d() {
for (int i = 0; i < 5; i++) {
a2d[i] = new int[10];
}
for (int i = 0; i < 5; i++) {
for (int j = 0; j < 10; j++) {
a2d[i][j] = rand() % 10 + 1;
cout << a2d[i][j] << endl;
}
}
return *a2d;
}
int* matrices::multiply() {
}
it is required that I only use pointer type variables and pointer returning functions, though that doesn't change too much. I don't know how they should be multiplied, and because of that, I am not sure how many values will be generated from the multiplication for the size of the new array. Thanks in advance!
Here is what I have designed to multiply them together. I have changed how my pointer arrays are allocated. My problem now is that it tells me that "expression must have arithmetic or unscoped enum type". Where I have matrix[i] =(a1d[index1] * a2d[index1][index2]); I thought maybe a1d needed to be a pointer type but it gives me the error where it can't convert from int* to int.
Also, when I debug, my a1d and matrix arrays allocate perfectly and show the correct number of data slots when moused over. However, a2d only shows one pointer which points to 5 in this case. I followed the syntax I have seen online for an array of pointers to create a 2d array.
int* matrices::filla1d() {
for (int i = 0; i < 5; i++) {
a1d[i] = new int;
}
for (int i = 0; i < 5; i++) {
*a1d[i] = rand() % 10 + 1;
}
return *a1d;
}
int* matrices::filla2d() {
for (int i = 0; i < 5; i++) {
a2d[i] = new int[10];
}
for (int i = 0; i < 5; i++) {
for (int j = 0; j < 10; j++) {
a2d[i][j] = rand() % 10 + 1;
}
}
return *a2d;
}
int* matrices::multiply() {
for (int i = 0; i < 50; i++) {
matrix[i] = new int;
}
int index1 = 0;
int index2 = 0;
for (int i = 0; i < 50; i++) {
matrix[i] = (a1d[index1] * a2d[index1][index2]);
index1++;
index2++;
}
return *matrix;
}
class matrices
{
private:
int* a1d[5];
int** a2d = new int*[5];
public:
int* matrix[50];
matrices();
~matrices();
int* filla1d();
int* filla2d();
int* multiply();
};
Edit 2:
I changed the line to fill up the new matrix to say
*matrix[i] = a2d[index1][index2] * *a1d[index1];
Now I get an access violation error on this line. I have matrix allocated the same way I have a1d allocated, what can cause my access violation?