Java Program to Multiply two Matrix Using Multi-dimensional Arrays


A quick and practical guide to multiply two matrices in java using multi dimensional array with 3 for loops. Example program without using threads.

1. Overview

In this tutorial, you'll learn how to multiply two matrix in java using multi dimensional arrays.

To understand this example program, it is better to know the following concepts.

Arrays - How to Initialize Arrays

For Loops Examples

Java Program to Multiply two Matrix Using Multi-dimensional Arrays

One condition must be satisfied for matrix multiplication as below.

First matrix order: R1 X C1

Second matrix order: R2 X C2

Always C1 and R2 must be same number that means number of columns in matrix 1 should be equal to the number of rows in the second matrix.

If this condition is not satisfied then matrix multiplication is not possible.

And also output matrix order will be R1 X C2.

2. Example Program To Multiply Two Matrices

Let us understand the below program that uses 3 for loops and with time complexity of Big O of n cube (O(n3)).

package com.javaprogramto.programs.arrays.matrix;

public class MatrixMultiplication {

	public static void main(String[] args) {
		// creating the first matrix using arrays
		int[][] matrix1 = { { 1, 2, 3 }, { 4, 5, 6 } };

		// creating the second matrix using two dimension array
		int[][] matrix2 = { { 1, 1 }, { 1, 1 }, { 1, 1 } };

		// Matrix 1 rows and columns length
		int rows1 = matrix1.length;
		int columns1 = matrix1[0].length;

		// Matrix 2 rows and columns length
		int rows2 = matrix2.length;
		int columns2 = matrix2[1].length;

		// output array for storing the multiplication result
		int[][] result = new int[rows1][columns2];

		// matrix addition core logic
		for (int i = 0; i < rows1; i++) {
			for (int j = 0; j < columns2; j++) {
				for (int k = 0; k < columns1; k++) {
					result[i][j] += matrix1[i][k] * matrix2[k][j];

		// printing the result
		for (int i = 0; i < result.length; i++) {
			for (int j = 0; j < result[1].length; j++) {
				System.out.print(result[i][j] + " ");





6 6 
15 15 


This examples works well for smaller inputs but if the order of these matrix's are 10 X 10 or 30 X 30 then it will give worst performance. So, you should optimize the code using multithreading.

Next article on Java Matrix Multiplication with multiple threads

3. Conclusion

In this article, you've seen how to multiply two matrices in java with using 3 for loops.

As usual, example shown is over GitHub.




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Author: Venkatesh - I love to learn and share the technical stuff.

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JavaProgramTo.com: Java Program to Multiply two Matrix Using Multi-dimensional Arrays
Java Program to Multiply two Matrix Using Multi-dimensional Arrays
A quick and practical guide to multiply two matrices in java using multi dimensional array with 3 for loops. Example program without using threads.
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