// Matr.java: multiply matrices, with returns
public class Matr {

   // C = A*B, mult of 4-by-4 matrices
   int[][] mult(int A[][], int B[][]){
      int[][] C = new int[4][4];
      for (int i = 0; i < 4; i++) { //rows
         for (int j = 0; j < 4; j++) { //cols
            C[i][j] = 0;
            for (int k = 0; k < 4; k++)
               C[i][j] += A[i][k] * B[k][j];
         }
      }
      return C;
   }

   void printMat(int A[][]){
      for (int i = 0; i < 4; i++){
         System.out.print("|");
         for (int j = 0; j < 4; j++)
           System.out.print(" "+A[i][j]+" ");
         System.out.print("|\n");
      }
      System.out.print("\n");
   }

   public static void main(String[] argv) {
      Matr matr = new Matr();
      int [][] A = {{2, 3, 1, 6},
                    {4, 0, 0, 2},
                    {4, 2, 0, 1},
                    {0, 3, 5, 2}};
      int [][] B = {{3, 0, 4, 3},
                    {1, 2, 0, 2},
                    {0, 3, 1, 4},
                    {5, 1, 3, 2}};
      int [][] C = matr.mult(A, B);
      matr.printMat(A);
      matr.printMat(B);
      matr.printMat(C);
   }
}

// Matr2.java: multiply matrices, with returns
public class Matr2 {

   // C = A*B, mult of 2-by-2 matrices
   int[][] mult(int A[][], int B[][]){
      int[][] C = new int[2][2];
      for (int i = 0; i < 2; i++) { //rows
         for (int j = 0; j < 2; j++) { //cols
            C[i][j] = 0;
            for (int k = 0; k < 2; k++)
               C[i][j] += A[i][k] * B[k][j];
         }
      }
      return C;
   }

   // C = A + B, addition of 2-by-2 matrices
   int[][] add(int A[][], int B[][]){
      int[][] C = new int[2][2];
      for (int i = 0; i < 2; i++) { //rows
         for (int j = 0; j < 2; j++) { //cols
            C[i][j] = A[i][j] + B[i][j];
         }
      }
      return C;
   }

   void printMat(int A[][]){
      for (int i = 0; i < 2; i++){
         System.out.print("|");
         for (int j = 0; j < 2; j++)
           System.out.print(" "+A[i][j]+" ");
         System.out.print("|\n");
      }
      System.out.print("\n");
   }

   public static void main(String[] argv) {
      Matr2 matr = new Matr2();
      int [][] A11 = {{2, 3},
                      {4, 0}};
      int [][] A12 = {{1, 6},
                      {0, 2}};
      int [][] A21 = {{4, 2},
                      {0, 3}};
      int [][] A22 = {{0, 1},
                      {5, 2}};
      int [][] B11 = {{3, 0},
                      {1, 2}};
      int [][] B12 = {{4, 3},
                      {0, 2}};
      int [][] B21 = {{0, 3},
                      {5, 1}};
      int [][] B22 = {{1, 4},
                      {3, 2}};
      int [][] C11 = 
          matr.add(matr.mult(A11, B11),
                   matr.mult(A12, B21));
      matr.printMat(A11);
      matr.printMat(B11);
      matr.printMat(A12);
      matr.printMat(B21);
      matr.printMat(C11);
      System.out.println("-----------");
      int [][] C12 =
          matr.add(matr.mult(A11, B12),
                   matr.mult(A12, B22));
      matr.printMat(A11);
      matr.printMat(B12);
      matr.printMat(A12);
      matr.printMat(B22);
      matr.printMat(C12);
      System.out.println("-----------");
      int [][] C21 =
          matr.add(matr.mult(A21, B11),
                   matr.mult(A22, B21));
      matr.printMat(A21);
      matr.printMat(B11);
      matr.printMat(A22);
      matr.printMat(B21);
      matr.printMat(C21);
      System.out.println("-----------");
      int [][] C22 =
          matr.add(matr.mult(A21, B12),
                   matr.mult(A22, B22));
      matr.printMat(A21);
      matr.printMat(B12);
      matr.printMat(A22);
      matr.printMat(B22);
      matr.printMat(C22);
      System.out.println("-----------");
   }
}

| 2  3  1  6 |        
| 4  0  0  2 |        | A11  A12 |
| 4  2  0  1 | = A =  | A21  A22 |
| 0  3  5  2 |

| 3  0  4  3 |
| 1  2  0  2 |        | B11  B12 |
| 0  3  1  4 | = B =  | B21  B22 |
| 5  1  3  2 |

| 39  15  27  28 |
| 22   2  22  16 |            | C11  C12 |
| 19   5  19  18 | = A * B =  | C21  C22 |
| 13  23  11  30 |


   A11   *    B11     +      A12   *    B21    =      C11

| 2  3 |   | 3  0 |       | 1  6 |   | 0  3 |     | 39  15 |
| 4  0 | * | 1  2 |   +   | 0  2 | * | 5  1 |  =  | 22   2 |


   A11   *    B12     +      A12   *    B22    =      C12

| 2  3 |   | 4  3 |       | 1  6 |   | 1  4 |     | 27  28 |
| 4  0 | * | 0  2 |   +   | 0  2 | * | 3  2 |  =  | 22  16 |


   A21   *    B11     +      A22   *    B21    =      C21

| 4  2 |   | 3  0 |       | 0  1 |   | 0  3 |     | 19   5 |
| 0  3 | * | 1  2 |   +   | 5  2 | * | 5  1 |  =  | 13  23 |


   A21   *    B12     +      A22   *    B22    =      C22

| 4  2 |   | 4  3 |       | 0  1 |   | 1  4 |     | 19  18 |
| 0  3 | * | 0  2 |   +   | 5  2 | * | 3  2 |  =  | 11  30 |