# Java Program to Multiply to Matrix Using Multi-dimensional Arrays

In this program, you'll learn to multiply two matrices using multi-dimensional arrays in Java.

To understand this example, you should have the knowledge of the following Java programming topics:

For matrix multiplication to take place, the number of columns of first matrix must be equal to the number of rows of 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]`

You can also multiply two matrices using functions.

## Example: Program to Multiply Two Matrices

``````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 = 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];
}
}
}

// Displaying the result
System.out.println("Sum of two matrices is: ");
for(int[] row : product) {
for (int column : row) {
System.out.print(column + "    ");
}
System.out.println();
}
}
}``````

Output

```Sum of two matrices is:
24    29
6    25    ```

In the above program, 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    _|
```