A matrix can be thought of as a multi-dimensional array. For example, a 2D array may also be referred to as a matrix (a table of rows and columns). And the initialization would look something like this

int matrix[2][3] = { { 1, 7, 3 }, { 2, 9, 6 } };

The concept of recursion is actually simple but implementing it is more challenging than you might think. Recursion works by creating a function that calls itself until it hits a base case to end/breakout of the recursion function. Along with the base case, it has another case that slowly leads to the base case.

A simple implementation of this can be seen with a function that gets the factorial value given a certain number.

Here is what that function looks like:

// Factorial function using recursion
int factorial(int n)
{
    // Base case for when the number given is 0
    if (n == 0)
    {
        return 1;
    }
 
    // Takes the given value and multiplies it by the previous factorial value
    else
    {
        // Function calls itself (calls n-1) until it reaches the base case (0)
        return n * factorial(n - 1);
    }
}

As you can see the function starts with the base case and then actually implements the logic for the function. Let's give n a value of 3. First, we are going to check if n is 0 and when it fails that check it will return 3*factorial(2), and then it will evaluate when n is 2. This pattern will continue until it evaluates n being 0. Now that the function has not been called again it returns 1 because n is 0. Now factorial(1) can complete its return, then factorial(2), and finally factorial(3). The result of factorial(3) is 6.