Arrays · Lesson 14 of 42

2D Arrays and Matrix Programs

5 min read Updated Nov 7, 2026 Saurabh Samir

On this page

Creating a 2-D array
Looping over rows and columns
Jagged arrays
Matrix programs
Practice
Summary

A two-dimensional array is an array of arrays – perfect for anything laid out in rows and columns: a seating plan, a marks sheet with subjects as columns, a game board or a mathematical matrix. Matrix programs are a staple of campus coding tests, so this lesson ends with the four you are most likely to meet.

In this lesson

Creating 2-D arrays and accessing [row][col]
Nested loops over rows and columns
Jagged arrays (rows of different lengths)
Matrix addition, transpose, multiplication and spiral order

Creating a 2-D array

import java.util.Arrays;

public class Main {
    public static void main(String[] args) {
        int[][] marks = {
            {78, 85, 90},     // student 0: maths, science, english
            {65, 72, 80},     // student 1
        };
        System.out.println(marks[1][2]);           // row 1, column 2
        System.out.println("rows: " + marks.length + ", cols: " + marks[0].length);
        int[][] grid = new int[2][3];              // all zeros
        grid[0][1] = 5;
        System.out.println(Arrays.deepToString(grid));
    }
}

Output

80
rows: 2, cols: 3
[[0, 5, 0], [0, 0, 0]]

int[][] marks – an array of row arrays

marks→ an array of 2 references
marks[0] → [78, 85, 90]row 0 is itself an int[]
marks[1] → [65, 72, 80]marks[1][2] is 80

Looping over rows and columns

public class Main {
    public static void main(String[] args) {
        String[] subjects = {"Maths", "Science", "English"};
        int[][] marks = {{78, 85, 90}, {65, 72, 80}, {92, 88, 79}};

        for (int s = 0; s < marks.length; s++) {
            int total = 0;
            for (int c = 0; c < marks[s].length; c++) total += marks[s][c];
            System.out.println("Student " + (s + 1) + " total: " + total);
        }
        for (int c = 0; c < subjects.length; c++) {
            int sum = 0;
            for (int[] row : marks) sum += row[c];
            System.out.printf("%s average: %.1f%n", subjects[c], sum / (double) marks.length);
        }
    }
}

Output

Student 1 total: 253
Student 2 total: 217
Student 3 total: 259
Maths average: 78.3
Science average: 81.7
English average: 83.0

Jagged arrays

Because each row is a separate array, rows can have different lengths – useful for things like Pascal's triangle or attendance where months have different numbers of days:

public class Main {
    public static void main(String[] args) {
        int rows = 5;
        int[][] pascal = new int[rows][];
        for (int r = 0; r < rows; r++) {
            pascal[r] = new int[r + 1];
            pascal[r][0] = pascal[r][r] = 1;
            for (int c = 1; c < r; c++) pascal[r][c] = pascal[r - 1][c - 1] + pascal[r - 1][c];
        }
        for (int[] row : pascal) {
            StringBuilder sb = new StringBuilder();
            for (int v : row) sb.append(v).append(' ');
            System.out.println(sb.toString().trim());
        }
    }
}

Output

Common mistake: assuming every row has the same length

Loop with matrix[r].length, not matrix[0].length, for the inner loop. With jagged arrays the second version throws ArrayIndexOutOfBoundsException or skips elements.

Matrix programs

Addition and transpose

import java.util.Arrays;

public class Main {
    public static void main(String[] args) {
        int[][] a = {{1, 2, 3}, {4, 5, 6}};
        int[][] b = {{6, 5, 4}, {3, 2, 1}};
        int[][] sum = new int[2][3];
        for (int i = 0; i < 2; i++)
            for (int j = 0; j < 3; j++) sum[i][j] = a[i][j] + b[i][j];
        System.out.println(Arrays.deepToString(sum));

        int[][] t = new int[3][2];               // rows and columns swap
        for (int i = 0; i < 2; i++)
            for (int j = 0; j < 3; j++) t[j][i] = a[i][j];
        System.out.println(Arrays.deepToString(t));
    }
}

Output

[[7, 7, 7], [7, 7, 7]]
[[1, 4], [2, 5], [3, 6]]

Multiplication

For A (m × n) times B (n × p), each result cell is the dot product of a row of A and a column of B – three nested loops:

import java.util.Arrays;

public class Main {
    public static void main(String[] args) {
        int[][] a = {{1, 2}, {3, 4}};
        int[][] b = {{5, 6}, {7, 8}};
        int n = a.length, m = b[0].length, k = b.length;
        int[][] c = new int[n][m];
        for (int i = 0; i < n; i++)
            for (int j = 0; j < m; j++)
                for (int x = 0; x < k; x++) c[i][j] += a[i][x] * b[x][j];
        System.out.println(Arrays.deepToString(c));
    }
}

Output

[[19, 22], [43, 50]]

Spiral order

A favourite of product-company interviews: walk the matrix in a spiral by shrinking four boundaries.

import java.util.ArrayList;
import java.util.List;

public class Main {
    public static void main(String[] args) {
        int[][] m = {{1, 2, 3, 4}, {5, 6, 7, 8}, {9, 10, 11, 12}};
        List<Integer> out = new ArrayList<>();
        int top = 0, bottom = m.length - 1, left = 0, right = m[0].length - 1;
        while (top <= bottom && left <= right) {
            for (int c = left; c <= right; c++) out.add(m[top][c]);
            top++;
            for (int r = top; r <= bottom; r++) out.add(m[r][right]);
            right--;
            if (top <= bottom) { for (int c = right; c >= left; c--) out.add(m[bottom][c]); bottom--; }
            if (left <= right) { for (int r = bottom; r >= top; r--) out.add(m[r][left]); left++; }
        }
        System.out.println(out);
    }
}

Output

[1, 2, 3, 4, 8, 12, 11, 10, 9, 5, 6, 7]

Practice

Try it yourself

Print the sum of both diagonals of a 3 × 3 matrix {{1,2,3},{4,5,6},{7,8,9}}.

Show solution

public class Main {
    public static void main(String[] args) {
        int[][] m = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};
        int primary = 0, secondary = 0;
        for (int i = 0; i < m.length; i++) {
            primary += m[i][i];
            secondary += m[i][m.length - 1 - i];
        }
        System.out.println(primary + " " + secondary);
    }
}

Output

15 15

Rotate a 3 × 3 matrix 90° clockwise into a new matrix.

Show solution

import java.util.Arrays;

public class Main {
    public static void main(String[] args) {
        int[][] m = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};
        int n = m.length;
        int[][] r = new int[n][n];
        for (int i = 0; i < n; i++)
            for (int j = 0; j < n; j++) r[j][n - 1 - i] = m[i][j];
        System.out.println(Arrays.deepToString(r));
    }
}

Output

[[7, 4, 1], [8, 5, 2], [9, 6, 3]]

Quick check

How do you get the number of columns in row 2 of grid?

grid[2].length

What is a jagged array?

A 2-D array whose rows have different lengths, possible because each row is a separate array.

How do you print a 2-D array's contents?

Arrays.deepToString(matrix)

Summary

A 2-D array is an array of row arrays: m[row][col].
Loop rows with m.length and columns with m[r].length; rows may differ (jagged).
Know addition, transpose, multiplication and spiral traversal for coding rounds.

Interview practice: Java coding interview programs.

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