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

(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 cij is ai1 × b1j + ai2 × b2j + c + ain × bnj.

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

where cij = ai1 * b1j+ ai2 * b2j+ ai3 * b3j.

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