Matrix Multiplication Program JAVA » CDACian


Matrix Multiplication Program

Consider the program of matrix multiplication in which the two matrices are multiplied with the use of three nested loops. We can multiply two matrices in java using binary * operator and executing another loop. A matrix is also known as array of arrays. We can add, subtract and multiply matrices.

In case of matrix multiplication, one row element of first matrix is multiplied by all columns of second matrix. Let the first matrix be of the order 3X3 and second matrix be of the order of 3X2. Since both the no. of columns in first matrix and no. of rows in second matrix are equal i.e. 3, the two matrices can be multiplied with each other and the resultant matrix will be of the order 3X2 (rows in first matrix and columns in second matrix).

 import java.util.Scanner;  
 class MatrixMulDemo  
      public static void main(String[] args)  
           //make a scanner for rows and columns  
           Scanner scan = new Scanner(;  
           System.out.println("Enter the number of rows for first matrix");  
           //store rows in a variable  
           int rowsFirst = scan.nextInt();  
           System.out.println("Enter the number of columns for first matrix / rows of   
 second matrix (they must be same for matrix multiplication");  
           //store columns in a variable  
           int colFirstRowSec = scan.nextInt();  
           System.out.println("Enter the columns for second matrix");  
           //store columns of second matrix in a variable  
           int colSec = scan.nextInt();  
           //make two dimensional arrays for storing the matrices elements  
           int[][] first = new int[rowsFirst][colFirstRowSec];  
           int[][] second = new int[colFirstRowSec][colSec];  
           System.out.println("Enter the values of first matrix");  
           for(int i=0; i<first.length; i++)  
                for(int j=0; j<first[0].length; j++)  
                     first[i][j] = scan.nextInt();  
           System.out.println("Enter the values of second matrix");  
           for(int i=0; i<second.length; i++)  
                for(int j=0; j<second[0].length; j++)  
                     second[i][j] = scan.nextInt();  
           //define the third resultant matrix  
           int result[][] = new int[rowsFirst][colSec];  
           //multiply the two matrices using three nested loops  
           for(int i=0; i<rowsFirst; i++)  
                for(int j=0; j<colSec; j++)  
                     for(int k=0; k<colFirstRowSec; k++)  
                          result[i][j] = result[i][j] + first[i][k] * second  
           //print all the elements of result matrix  
           System.out.println("Product of two matrices ");  
           for(int i=0; i<result.length; i++)  
                for(int j=0; j<result[0].length; j++)  
                     System.out.print(result[i][j] + " ");  
                //for line gap  

Alternative Solution

Let's see a simple example to multiply two matrices of 3 rows and 3 columns.

public class MatrixMultiplicationExample{  
public static void main(String args[]){  
//creating two matrices    
int a[][]={{1,1,1},{2,2,2},{3,3,3}};    
int b[][]={{1,1,1},{2,2,2},{3,3,3}};    
//creating another matrix to store the multiplication of two matrices    
int c[][]=new int[3][3];  //3 rows and 3 columns  
//multiplying and printing multiplication of 2 matrices    
for(int i=0;i<3;i++){    
for(int j=0;j<3;j++){    
for(int k=0;k<3;k++)      
}//end of k loop  
System.out.print(c[i][j]+" ");  //printing matrix element  
}//end of j loop  
System.out.println();//new line    


6 6 6 

12 12 12 

18 18 18 

Additional Coding Logic

public class MultiplyMatrices {

    public static void main(String[] args) {
        int r1 = 2, c1 = 3;
        int r2 = 3, c2 = 2;
        int[][] firstMatrix = { {3, -2, 5}, {3, 0, 4} };
        int[][] secondMatrix = { {2, 3}, {-9, 0}, {0, 4} };

        // Mutliplying Two matrices
        int[][] product = new int[r1][c2];
        for(int i = 0; i < r1; i++) {
            for (int j = 0; j < c2; j++) {
                for (int k = 0; k < c1; k++) {
                    product[i][j] += firstMatrix[i][k] * secondMatrix[k][j];

        // Displaying the result
        System.out.println("Multiplication of two matrices is: ");
        for(int[] row : product) {
            for (int column : row) {
                System.out.print(column + "    ");
Multiplication of two matrices is:
24    29    
6    25  

In general,

M(ixj) * M(jxk) = M(ixk)

To multiply the two matrices we need to multiply the rows of first matrix to the columns of second matrix as shown below in the diagram.

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