To multiply matrix a by matrix b, the number of columns in a must be the same *
* as the number of rows in b, and the two matrices must have elements of the same*
* or compatible types. Let c be the result of the multiplication. Assume the *
* column size of matrix a is n. Each element cij is ai1 * b1j + ai2 * b2j + ... *
* + ain * bnj. *
* *
* Write a test program that prompts the user to enter two 3 * 3 matrices and *
* displays their product.

I am writing JAVA program:        

import java.util.Scanner;   // to take input from user

public class MatrixMultiplication {  

public static void main(String[] args) {  // start of main function      

double[][] matrixA = new double[3][3];  // matrix 1

       double[][] matrixB = new double[3][3];   // matrix 2

Scanner input = new Scanner(System.in);   // scans user input

System.out.print("Enter matrix A: ");   // prompts to enter matrix A

 for (int i = 0; i < matrixA.length; i++) {  

           //loop to enter values in matrix A till length of matrixA

 for (int j = 0; j < matrixA.length; j++)

             // reads the matrixA values entered by the user

   matrixA[i][j] = input.nextDouble();  }

System.out.print("Enter matrix B: ");  // prompts to enter matrix B

           //loop to enter values in matrix B till length of matrixB

               for (int i = 0; i < matrixB.length; i++) {

 for (int j = 0; j < matrixB.length; j++)

             // reads the matrixB values entered by the user

   matrixB[i][j] = input.nextDouble();}

 //matrixC stores the result of the product of matrixA and matrixB  

    double[][] matrixC = Multiplication(matrixA, matrixB);  

         // Display function is called to display the matrices A, B and product //result which is matrixC

    Display(matrixA, matrixB, matrixC);  }  

      //function Multiplication to calculate the product of matrixA and matrixB

public static double[][] Multiplication(double[][] inputMatrix1, double[][] inputMatrix2) {

              //stores the product of two matrices

 double[][] outputMatrix = new double[3][3];  

      //the loops below are used to move through the rows of outputMatrix

 for (int i = 0; i < outputMatrix.length; i++) {

 for (int j = 0; j < outputMatrix[i].length; j++) {

   for (int k = 0; k < outputMatrix.length; k++) {

/* takes the product of inputMatrix1 and inputMatrix2 and adds result of product of each row and stores the result in matrix outputMatrix*/

 outputMatrix[i][j] += inputMatrix1[i][k] * inputMatrix2[k][j];

   }    }   }

 return outputMatrix;  }  //returns the resultant matrix

public static void resultMatrix(double[][] matrix, int row) {

             //displays all the values in row form

 for (int j = 0; j < matrix[row].length; j++) {

 System.out.printf("%.1f", matrix[row][j]);  }  }

public static void Display(double[][] matrix1, double[][] matrix2, double[][] matrix3) {    //displays the result of product of two matrices  

 System.out.println("The product of two 3*3 matrices is: ");    

        for (int i = 0; i < 3; i++) {

 resultMatrix(matrix1, i);  //displays elements of matrix A

 System.out.print((i == 1 ? "   * " : "     "));

 resultMatrix(matrix2, i);  //displays elements of matrix B

 System.out.print((i == 1 ? "   = " : "     "));

 resultMatrix(matrix3, i);  //displays elements of resultant matrixC

 System.out.println();  }  }  }

Explanation:

The program has three functions and main() function. In the main() function programs prompts the user to enter the elements of matrix A and matrix B and uses Scanner class to take this input from the user. Then Multiplication() function is called which computes the product of the two 3*3 matrices i.e. matrixA and matrixB and stores the result in matrixC. Next Display() function is called which displays the elements of matrix A, matrix B and the resultant matrix C in the matrix form with * between matrix A and B and the = sign between the input matrices and their product matrix.

The output of the program is attached as screen shot.