(Algebra: add two matrices) Write a method to add two matrices. The header of the method is as follows:

public static double [][] addMatrix(double[] [] a , double[][] b)

In order to be added, the two matrices must have the same dimensions and the same or compatible types of elements. Let c be the resulting matrix. Each element c_ij is a_ij + b_ij. For example, for two 3 × 3 matrices a and b, c is

     ( a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 ) + ( b 11 b 12 b 13 b 21 b 22 b 23 b 31 b 32 b 33 ) = ( a 11 + b 11 a 12 + b 12 a 13 + b 13 a 21 + b 21 a 22 + b 22 a 23 + b 23 a 31 + b 31 a 32 + b 32 a 33 + b 33 )

Write a test program that prompts the user to enter two 3 × 3 matrices and displays their sum. Here is a sample run: