A 2D array is not a rectangular grid. Or maybe better, there is no such thing as a 2D array in Java.

import java.util.Arrays;

public class Main {
  public static void main(String args[]) {

    int[][] test; 
    test = new int[5][];//'2D array'
    for (int i=0;i<test.length;i++)
      test[i] = new int[i];

    System.out.println(Arrays.deepToString(test));

    Object[] test2; 
    test2 = new Object[5];//array of objects
    for (int i=0;i<test2.length;i++)
      test2[i] = new int[i];//array is a object too

    System.out.println(Arrays.deepToString(test2));
  }
}

Outputs

[[], [0], [0, 0], [0, 0, 0], [0, 0, 0, 0]]
[[], [0], [0, 0], [0, 0, 0], [0, 0, 0, 0]]

The arrays test and test2 are (more or less) the same.

It's important to understand that Java doesn't really have two-dimensional arrays. It has arrays of arrays. That means, for instance, that you can have this:

int[][] array=
{
    {1},
    {1, 2, 3},
    {1, 2, 3, 4, 5},
    {1, 2}
};

So there is no one upper bound of the second level. Java arrays are inherently jagged, each of the second level in the above has its own length.

So to loop them correctly, you have to check for each of the second-level arrays:

int x, y;
int[] second;

for (x = 0; x < array.length; ++x) {
    second = array[x];
    for (y = 0; y < second.length; ++y) {
         // ....
    }
}

Full example: Live Copy

public class ArrayExample {
    public static void main(String[] args) {
        int[][] array=
        {
            {1},
            {1, 2, 3},
            {1, 2, 3, 4, 5},
            {1, 2}
        };
        int x, y;
        int[] second;

        for (x = 0; x < array.length; ++x) {
          second = array[x];
          for (y = 0; y < second.length; ++y) {
              System.out.println(x + "," + y + ": " + second[y]);
          }
          System.out.println();
        }
    }
}

Output:

0,0: 1

1,0: 1
1,1: 2
1,2: 3

2,0: 1
2,1: 2
2,2: 3
2,3: 4
2,4: 5

3,0: 1
3,1: 2

Or if you don't need the indexes, just the values, you can use the enhanced for loop: Live Example

public class ArrayExample {
    public static void main(String[] args) {
        int[][] array=
        {
            {1},
            {1, 2, 3},
            {1, 2, 3, 4, 5},
            {1, 2}
        };

        for (int[] second : array) {
          for (int entry : second) {
              System.out.println(entry);
          }
          System.out.println();
        }
    }
}

Output:

1

1
2
3

1
2
3
4
5

1
2

Java technically doesn't have 2-dimensional arrays, it has arrays of arrays.

 System.out.println(example.length); // number of rows
 System.out.println(example[0].length); // number of columns in first row

But This could fail if:

1. array size is 0, in which you will get an exception.
2. You are explicitly assuming that size of first element of array as size of rows, this could be ambiguous if you are taking a Jagged array.

Jagged Array: Jagged array is array of arrays such that member arrays can be of different sizes, i.e., we can create a 2-D arrays but with variable number of columns in each row.

you can think of the following array variable as array of arrays, it consists of 3 arrays each of which contain 4 elements

int [][]array = new int[3][4];

so when you try array.length you get 3 the first array that contains 3 arrays which contain 4 elements each, however when you array[0].length,array[1].length, array[2].length, you are checking lengths of arrays of elements in array variable, which all give you 4.

Edit:

lets say you want to take out the arrays from array variable array and check lengths

int [] arr1 = array[0]; // arr1.length = array[0].length which is 4
int [] arr2 = array[1]; // arr2.length = array[1].length which is 4
int [] arr3 = array[2];  //arr3.length = array[2].length which is 4

Java doesn't have 2D arrays. Java has arrays of arrays. The second loop uses column < a[row].length to make sure that you don't iterate past the length of the row-th array. You need this to handle nested arrays of varying length.