For matrix multiplication to take place, the number of columns of the first matrix must be equal to the number of rows of the second matrix. In our example, i.e.

c1 = r2

Also, the final product matrix is of size r1 x c2, i.e.

product[r1][c2]

Example: Program to Multiply Two Matrices using a Function

public class MultiplyMatrices{

    public static void main(String[] args){
        int r1 = 2, c1 = 3;
        int r2 = 3, c2 = 2;
        int[][] firstMatrix = { {3, -2, 5}, {3, 0, 4} };
        int[][] secondMatrix = { {2, 3}, {-9, 0}, {0, 4} };

        // Mutliplying Two matrices
        int[][] product = multiplyMatrices(firstMatrix, secondMatrix, r1, c1, c2);

        // Displaying the result
        displayProduct(product);
    }

    public static int[][] multiplyMatrices(int[][] firstMatrix, int[][] secondMatrix, int r1, int c1, int c2) {
        int[][] product = new int[r1][c2];
        for(int i = 0; i < r1; i++) {
            for (int j = 0; j < c2; j++) {
                for (int k = 0; k < c1; k++) {
                    product[i][j] += firstMatrix[i][k] * secondMatrix[k][j];
                }
            }
        }

        return product;
    }

    public static void displayProduct(int[][] product){
        System.out.println("Product of two matrices is: ");
        for(int[] row : product) {
            for (int column : row) {
                System.out.print(column + "    ");
            }
            System.out.println();
        }
    }
}

Output

Product of two matrices is:
24    29    
6    25    

In the above program, there are two functions:

• multiplyMatrices() which multiplies the two given matrices and returns the product matrix
• displayProduct() which displays the output of the product matrix on the screen.

The multiplication takes place as:

|-    (a11 x b11) + (a12 x b21) + (a13 x b31)    (a11 x b12) + (a12 x b22) + (a13 x b32)    -|
|_    (a21 x b11) + (a22 x b21) + (a23 x b31)    (a21 x b12) + (a22 x b22) + (a23 x b32)    _|

In our example, it takes place as:

|-    (3 x 2) + (-2 x -9) + (5 x 0) = 24    (3 x 3) + (-2 x 0) + (5 x 4) = 29    -|
|_    (3 x 2) + ( 0 x -9) + (4 x 0) = 6    (3 x 3) + ( 0 x 0) + (4 x 4) = 25    _|