How do you write an algorithm for the multiplication of two matrix [2D array]?

Problem statement:
Given two matrices, the task is to multiply them. Matrices can either be square or rectangular.
Example:
Input: int m1[][] = {{2, 3, 4}, {5, 6, 7}}; // 2 X 3 matrix
int m2[][] = {{1, 2}, {3, 4}, {5, 6}}; // 3 X 2 matrix
Output: {{31, 40},{58,76}}

1. public class MatrixMultiplication {
2.     public static void main(String args[]) {
3.         int m1[][] = {{2, 3, 4}, {5, 6, 7}};    // 2 X 3 matrix
4.         int m2[][] = {{1, 2}, {3, 4}, {5, 6}};  // 3 X 2 matrix
5.         int res[][] = new int[2][2];    // resultant matrix of 2 X 2
6.         for (int i = 0; i < 2; i++) {   // i represent row
7.             for (int j = 0; j < 2; j++) {   // j represent column
8.                 res[i][j] = 0;  // assume res[0][0] = 0
9.                 for (int k = 0; k < 3; k++) {
10.                     // k represent first matrix i.e. m1 -> number of column for                        // counter sum
11.                     res[i][j] = res[i][j] + m1[i][k] * m2[k][j];
12.                 }
13.             }
14.         }
15.         // printing the resultant matrix
16.         for (int i = 0; i < 2; i++) {
17.             for (int j = 0; j < 2; j++) {
18.                 System.out.print(res[i][j] + " ");
19.             }
20.             System.out.println();
21.         }
22.     }
23. }

Method-II:

1. public class MatrixMultiplication2D {
2.     public static void main(String args[]) {
3.         int m1[][] = {{2, 3, 4}, {5, 6, 7}};    // 2 X 3 matrix
4.         int m2[][] = {{1, 2}, {3, 4}, {5, 6}};  // 3 X 2 matrix
5.         int sum = 0;    // initial sum value is 0
6.         int res[][] = new int[2][2];    // resultant matrix of 2 X 2
7.         for (int i = 0; i < 2; i++) {   // i represent row
8.             for (int j = 0; j < 2; j++) {   // j represent column
9.                 res[i][j] = 0;  // assume res[0][0] = 0
10.                 for (int k = 0; k < 3; k++) {
11.                     // k represent first matrix i.e. m1 -> number of column for                        // counter sum
12.                     sum = sum + m1[i][k] * m2[k][j];
13.                 }
14.                 res[i][j] = sum;    //  assigned sum value to resultant matrix
15.                 sum = 0;    // reset to 0 for next iteration
16.             }
17.         }
18.         // printing the resultant matrix
19.         for (int i = 0; i < 2; i++) {
20.             for (int j = 0; j < 2; j++) {
21.                 System.out.print(res[i][j] + " ");
22.             }
23.             System.out.println();
24.         }
25.     }
26. }

Output:

31 40

58 76