pointer to array of ints c++

Question

I wrote the following code to try to understand how we can use pointers to arrays and references to arrays. Here is my thought process of what is happening.

1. arr is the same as the address of the first elements of the array. *arr gives me what is the int at that location as does arr[0].
2. p is a pointer and gets assigned arr which is the address of the first element. So in essence *p is the same as *arr and p[0] is the same as arr[0].
3. Here i don't understand what is happening. arrPtr is a pointer to an array of ten integers. Why doesn't *arrPtr or arrPtr[0] yield me the value 9?
4. arrRef is a reference to an array of ten integers and unlike in the point above *arrRef or arrRef[0] does yield value 9.

Here is my code:

#include <iostream>

using std::cin;
using std::cout;
using std::endl;

int main() {
    int arr[10] = {9, 18, 31, 40, 42};
    cout << "arr: " << arr << endl;
    cout << "*arr: " << *arr << endl;
    cout << "arr[0]: " << arr[0] << endl;
    cout << endl;

    int *p = arr;
    cout << "p: " << p << endl;
    cout << "*p: " << *p << endl;
    cout << "p[0]: " << p[0] << endl;
    cout << endl;

    int (*arrPtr)[10] = &arr;
    cout << "arrPtr: " << arrPtr << endl;
    cout << "*arrPtr: " << *arrPtr << endl;
    cout << "arrPtr[0]: " << arrPtr[0] << endl;
    cout << endl;

    int (&arrRef)[10] = arr;
    cout << "arrRef: " << arrRef << endl;
    cout << "*arrRef: " << *arrRef << endl;
    cout << "arrRef[0]: " << arrRef[0] << endl;
}

Here is my output:

arr: 0xbf843e28
*arr: 9
arr[0]: 9

p: 0xbf843e28
*p: 9
p[0]: 9

arrPtr: 0xbf843e28
*arrPtr: 0xbf843e28
arrPtr[0]: 0xbf843e28

arrRef: 0xbf843e28
*arrRef: 9
arrRef[0]: 9

Answer 1

*arrPtr or arrPtr[0] yields an object of the type int[10]

Used in the operator << the array is explicitly converted to pointer of type int * and the overloaded operator << for the parameter of const void * is selected for such an expression.

You can see that these outputs

arr: 0xbf843e28

and

*arrPtr: 0xbf843e28
arrPtr[0]: 0xbf843e28

coincide.

If you want to output the first element of the array you should write either

std::cout << **arrPtr << std::endl;
std::cout << ( *arrPtr )[0] << std::endl;
std::cout << arrPtr[0][0] << std::endl;
std::cout << *arrPtr[0] << std::endl;

To make it more clear you can introduce a reference such a way

int ( &arrRef )[10] = *arrPtr;

and then write

std::cout << *arrRef << std::endl;
std::cout << arrRef[0] << std::endl;