Chapter 8, Problem 8.6PE

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

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

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 c_ij is a_i1 × b_1j + a_i2 × b_2j + . . . + a_in × b_nj·

For example, for two 3 × 3 matrices a and b, c is

     $\left(\begin{array}{ccc}{a}_{11}& a_{12}& a_{13}\\ a_{21}& a_{22}& a_{23}\\ a_{31}& a_{32}& a_{33}\end{array}\right)\times \left(\begin{array}{ccc}{b}_{11}& b_{12}& b_{13}\\ b_{21}& b_{22}& b_{23}\\ b_{31}& b_{32}& b_{33}\end{array}\right)=\left(\begin{array}{ccc}{c}_{11}& c_{12}& c_{13}\\ c_{21}& c_{22}& c_{23}\\ c_{31}& c_{32}& c_{33}\end{array}\right)$

where c_ij = a_i1 × b_1j + a_i2 × b_2j + . . . + a_i3 × b_3j.

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