Matrix Addition in Java | Addition of two matrix in Java | Java program to add two matrices | Add two matrix in Java | In this post, we will see the Java program to find the matrix addition in Java.

Let A =[aij] and B =[bij] be m × n matrices. The sum of A and B, denoted by A + B, is the m × n matrix that has aij + bij as its (i, j)th element. In other words, A + B =[aij + bij].

The sum of two matrices of the same size is obtained by adding elements in the corresponding positions.

Condition for matrix addition:- Both matrices should have same row and column size.

Matrices of different sizes cannot be added, because the sum of two matrices is defined only when both matrices have the same number of rows and the same number of columns.

```     a11  a12
A =
a21  a22```
```     b11  b12
B =
b21  b22```

The addition of A and B can be calculated as,

`        a11+b11  a12+b12A + B =         a21+b21  a22+b22`

Java Method to find the sum of two matrices

```// method to calculate the addition of two matrix
public static int[][] addMatrix(int[][] a, int[][] b) {

// calculate row and column size of anyone matrix
int row = a.length;
int column = a.length;

// declare a matrix to store resultant value
int sum[][] = new int[row][column];

// calculate sum of two matrices
// outer loop for row
for(int i=0; i<row; i++) {

// inner loop for column
for(int j=0; j<column; j++) {

// formula
sum[i][j] = a[i][j] + b[i][j];
}
}

// return resultant matrix
return sum;
}```

Time Complexity:- O(N2)

The above Java method uses two loops to find the matrix addition therefore the time complexity for the method is O(N2).

## Program for Matrix Addition in Java

In this program, values for the matrices are already given just call the method to add both matrices, and then display the resultant matrix.

```import java.util.Arrays;

public class Matrix {

// main method
public static void main(String[] args) {

// declare and initialize two matrices
int a[][] = { { 1, 3 }, { 7, 5 } };
int b[][] = { { 6, 8 }, { 4, 2 } };

// find row and column size
// (Assuming both matrix have same size)
int row = a.length;
int column = a.length;

// declare new matrix to store result
int c[][] = new int[row][column];

// sum of matrix

// display all matrices
System.out.println("A = " + Arrays.deepToString(a));
System.out.println("B = " + Arrays.deepToString(b));
System.out.println("C = " + Arrays.deepToString(c));
}

// method to calculate the addition of two matrix
public static int[][] addMatrix(int[][] a, int[][] b) {

// calculate row and column size
int row = a.length;
int column = a.length;

// declare a matrix to store resultant
int sum[][] = new int[row][column];

// calculate sum of two matrices
// outer loop for row
for(int i=0; i<row; i++) {
// inner loop for column
for(int j=0; j<column; j++) {
// formula
sum[i][j] = a[i][j] + b[i][j];
}
}

// return resultant matrix
return sum;
}
}```

Output:-

A = `[[`1, 3`]`, `[`7, 5`]]`
B = `[[`6, 8`]`, `[`4, 2`]]`
C = `[[`7, 11`]`, `[`11, 7`]]`

In this program, to display the matrix we had used deepToString() method of the Arrays class, but you can also use the nested loops. See:- Different ways to print array in Java

## Program by taking Input from the User

In the above program both matrices A and B were initialized with in the program, now let us see an another Java program for matrix addition by taking input value from user using Scanner. If you want then you can also use BufferedReader class.

```import java.util.Scanner;

public class Matrix {

// create Scanner class object to read input
private static Scanner scan = new Scanner(System.in);

// main method
public static void main(String[] args) {

// declare variables
int row = 0;
int column = 0;
int a[][] = null; // first matrix
int b[][] = null; // second matrix
int c[][] = null; // resultant matrix

// ask row and column size
System.out.println("Enter row and column size: ");
row = scan.nextInt();
column = scan.nextInt();

// initialize matrices
a = new int[row][column];
b = new int[row][column];
c = new int[row][column];

// read matrix A and B
System.out.println("Enter Matrix A: ");
System.out.println("Enter Matrix B: ");

// sum of matrix

// display resultant matrix
System.out.println("Sum (C): ");
for(int i=0; i<c.length; i++) {
for(int j=0; j<c.length; j++) {
System.out.print(c[i][j]+" ");
}
System.out.println(); // new line
}
}

// method to read matrix elements as input
public static int[][] readMatrix(int[][] temp) {
for(int i=0; i<temp.length; i++) {
for(int j=0; j<temp.length; j++) {
temp[i][j] = scan.nextInt();
}
}
return temp;
}

// method to calculate the addition of two matrix
public static int[][] addMatrix(int[][] a, int[][] b) {
// calculate row and column size
int row = a.length;
int column = a.length;

// declare a matrix to store resultant
int sum[][] = new int[row][column];

// calculate sum of two matrices
// outer loop for row
for(int i=0; i<row; i++) {
// inner loop for column
for(int j=0; j<column; j++) {
// formula
sum[i][j] = a[i][j] + b[i][j];
}
}

// return resultant matrix
return sum;
}

}```

Output:-

Enter row and column size:
3 3
Enter Matrix A:
1 2 3
4 5 6
7 8 9
Enter Matrix B:
5 6 7
8 9 10
3 1 2
Sum (C):
6 8 10
12 14 16
10 9 11

In this program, we had created Scanner class object as a private static variable which is outside of the main method because we need to read input values in two methods, in main method to read row and column values and in readMatrix() method to read matrix elements. Therefore instead of creating Scanner class object in both classes separately, it is better to create them as a static variable only once and use it multiple times anywhere in the program.

See more matrix programs in Java:-

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