In Java write three methods for the matrix class that corres

 In Java write three methods for the matrix class that correspond to the three basic operations described below  addition: two matrices must be the same size; add corresponding elements to create a new matrix that holds the sum of the values in the origanl matrices  Scalar multiplication: all elements of a matrix are multiplied by a single number  transpose: the transpose of a matrix is a new matrix in which the elements of each row of the original matrix becomes the corresponding column of the new matrix  /**  * Matrix class describes operations on a matrix of integers  * @author Cate Sheller  * @version 8/30/2011  */ public class Matrix {     private int [][] grid;       /**      * default constructor: creates 3x3 matrix with random values      * in the range 0..9      */     public Matrix() {         grid = new int[3][3];         for(int x=0; x<3; x++)             for(int y=0; y<3; y++)                 grid[x][y] = (int)(Math.random()*10);     }     /**      * Creates matrix of specified size with random values 0..9      * @param size positive integer that represents the number of rows      * and columns in the matrix      */     public Matrix(int size) {         grid = new int[size][size];         for(int x=0; x<size; x++)             for(int y=0; y<size; y++)                 grid[x][y] = (int)(Math.random()*10);     }     /**       * Creates a matrix of specified size with random values 0..9      * @param rows number of rows in matrix      * @param columns number of columns int matrix      */     public Matrix(int rows, int columns) {         grid = new int[rows][columns];         for(int x=0; x<rows; x++)             for(int y=0; y<columns; y++)                 grid[x][y] = (int)(Math.random()*10);     }     /**      * @return String formatted as an m x n matrix of m rows and       * n columns      */     public String toString() {         int rows = grid.length;         int columns = grid[0].length;         String table = new String(\"\");         for(int x=0; x<rows; x++) {             table = table + \'|\' + \'\\t\';             for(int y=0; y<columns; y++)                 table = table + grid[x][y] + \'\\t\';             table = table + \'|\' + \'\ \';         }         return table;     }     /**      * @return true if number of rows equals number of columns      */     public boolean isSquare() {         return grid.length == grid[0].length;     }     /**      * @param other another matrix to compare to this one      * @return true if this matrix and the other have the same      * number of rows and columns      */     public boolean sameSize(Matrix other) {         return grid.length == other.grid.length &&                  grid[0].length == other.grid[0].length;     }     public static void main(String[] args) {         Matrix m = new Matrix();         Matrix n = new Matrix((int)(Math.random()*5)+2);         Matrix o = new Matrix(((int)(Math.random()*5)+2),                                                         ((int)(Math.random()*5)+2));         System.out.println (\"First matrix:\");         System.out.print(m);         System.out.println (\"Second matrix:\");         System.out.println(n);         System.out.println (\"Third matrix:\");         System.out.println(o);         if(m.sameSize(n))             System.out.println(\"First two are the same size\");         else             System.out.println(\"First two are not the same size\");         if(o.isSquare())             System.out.println(\"All three are square matrices\");         else             System.out.println(\"Only first two are square matrices\");     } }