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