The elements of an array can be of any data type, including arrays! An array of arrays is called a **multidimensional array**.

`int array[3][5]; // a 3-element array of 5-element arrays`

Since we have 2 subscripts, this is a two-dimensional array.

In a two-dimensional array, it is convenient to think of the first (left) subscript as being the row, and the second (right) subscript as being the column. This is called **row-major** order. Conceptually, the above two-dimensional array is laid out as follows:

[0][0] [0][1] [0][2] [0][3] [0][4] // row 0 [1][0] [1][1] [1][2] [1][3] [1][4] // row 1 [2][0] [2][1] [2][2] [2][3] [2][4] // row 2

To access the elements of a two-dimensional array, simply use two subscripts:

`array[2][3] = 7;`

**Initializing two-dimensional arrays**

To initialize a two-dimensional array, it is easiest to use nested braces, with each set of numbers representing a row:

```
int array[3][5]
{
{ 1, 2, 3, 4, 5 }, // row 0
{ 6, 7, 8, 9, 10 }, // row 1
{ 11, 12, 13, 14, 15 } // row 2
};
```

Although some compilers will let you omit the inner braces, we highly recommend you include them anyway, both for readability purposes and because of the way that C++ will replace missing initializers with 0.

```
int array[3][5]
{
{ 1, 2 }, // row 0 = 1, 2, 0, 0, 0
{ 6, 7, 8 }, // row 1 = 6, 7, 8, 0, 0
{ 11, 12, 13, 14 } // row 2 = 11, 12, 13, 14, 0
};
```

Two-dimensional arrays with initializer lists can omit (only) the leftmost length specification:

```
int array[][5]
{
{ 1, 2, 3, 4, 5 },
{ 6, 7, 8, 9, 10 },
{ 11, 12, 13, 14, 15 }
};
```

The compiler can do the math to figure out what the array length is. However, the following is not allowed:

```
int array[][]
{
{ 1, 2, 3, 4 },
{ 5, 6, 7, 8 }
};
```

Just like normal arrays, multidimensional arrays can still be initialized to 0 as follows:

`int array[3][5]{};`

**Accessing elements in a two-dimensional array**

Accessing all of the elements of a two-dimensional array requires two loops: one for the row, and one for the column. Since two-dimensional arrays are typically accessed row by row, the row index is typically used as the outer loop.

```
for (int row{ 0 }; row < numRows; ++row) // step through the rows in the array
{
for (int col{ 0 }; col < numCols; ++col) // step through each element in the row
{
std::cout << array[row][col];
}
}
```

In C++11, *for-each* loops can also be used with multidimensional arrays. We’ll cover for-each loops in detail later.

**Multidimensional arrays larger than two dimensions**

Multidimensional arrays may be larger than two dimensions. Here is a declaration of a three-dimensional array:

`int array[5][4][3];`

Three-dimensional arrays are hard to initialize in any kind of intuitive way using initializer lists, so it’s typically better to initialize the array to 0 and explicitly assign values using nested loops.

Accessing the element of a three-dimensional array is analogous to the two-dimensional case:

`std::cout << array[3][1][2];`

**A two-dimensional array example**

Let’s take a look at a practical example of a two-dimensional array:

```
#include <iostream>
int main()
{
constexpr int numRows{ 10 };
constexpr int numCols{ 10 };
// Declare a 10x10 array
int product[numRows][numCols]{};
// Calculate a multiplication table
// We don't need to calc row and col 0 since mult by 0 always is 0
for (int row{ 1 }; row < numRows; ++row)
{
for (int col{ 1 }; col < numCols; ++col)
{
product[row][col] = row * col;
}
}
// Print the table
for (int row{ 1 }; row < numRows; ++row)
{
for (int col{ 1 }; col < numCols; ++col)
{
std::cout << product[row][col] << '\t';
}
std::cout << '\n';
}
return 0;
}
```

This program calculates and prints a multiplication table for all values between 1 and 9 (inclusive). Note that when printing the table, the for loops start from 1 instead of 0. This is to omit printing the 0 column and 0 row, which would just be a bunch of 0s! Here is the output:

1 2 3 4 5 6 7 8 9 2 4 6 8 10 12 14 16 18 3 6 9 12 15 18 21 24 27 4 8 12 16 20 24 28 32 36 5 10 15 20 25 30 35 40 45 6 12 18 24 30 36 42 48 54 7 14 21 28 35 42 49 56 63 8 16 24 32 40 48 56 64 72 9 18 27 36 45 54 63 72 81

Two dimensional arrays are commonly used in tile-based games, where each array element represents one tile. They’re also used in 3d computer graphics (as matrices) in order to rotate, scale, and reflect shapes.