Matrix Addition in C: Program to Add Two Matrices

📚 In this tutorial, you will learn:

What is matrix addition and its conditions
How to add two matrices using nested loops
How to handle matrices with different dimensions
Step-by-step explanation of the program
Practice exercises to test your understanding

Introduction

In this tutorial, we will learn how to write a C program to add two matrices.

Matrix addition is a simple operation where we add corresponding elements of two matrices. It is a fundamental operation in linear algebra and is used in many applications.

💡 Key Point: Matrix addition is possible only when both matrices have the same dimensions (same number of rows and columns).

Matrix Addition Rule

Matrix A: Dimensions r × c
Matrix B: Dimensions r × c (must match)
Result Matrix C: Dimensions r × c
Formula: C[i][j] = A[i][j] + B[i][j]

Formula:

C[i][j] = A[i][j] + B[i][j]

Each element of the result matrix is the sum of corresponding elements from A and B.

Visual Example

Matrix A (2×3):

[1  2  3]
[4  5  6]

Matrix B (2×3):

[7   8   9]
[10  11  12]

Result C (2×3):

[8   10  12]
[14  16  18]

Calculation: C[0][0] = 1 + 7 = 8
C[0][1] = 2 + 8 = 10
C[0][2] = 3 + 9 = 12
C[1][0] = 4 + 10 = 14
C[1][1] = 5 + 11 = 16
C[1][2] = 6 + 12 = 18

Matrix addition is used in many real-world applications, such as:

Image Processing: Adding two images (overlay)
Data Analysis: Combining datasets
Physics: Adding vectors and matrices
Computer Graphics: Combining transformation matrices

C Program for Matrix Addition

#include <stdio.h>

int main() {
    int rows, cols, i, j;
    
    // Ask user for matrix dimensions
    printf("Enter the number of rows: ");
    scanf("%d", &rows);
    printf("Enter the number of columns: ");
    scanf("%d", &cols);
    
    // Declare matrices
    int A[rows][cols], B[rows][cols], C[rows][cols];
    
    // ====== READ FIRST MATRIX ======
    printf("\nEnter %d elements for first matrix:\n", rows * cols);
    for(i = 0; i < rows; i++) {
        for(j = 0; j < cols; j++) {
            printf("A[%d][%d] = ", i, j);
            scanf("%d", &A[i][j]);
        }
    }
    
    // ====== READ SECOND MATRIX ======
    printf("\nEnter %d elements for second matrix:\n", rows * cols);
    for(i = 0; i < rows; i++) {
        for(j = 0; j < cols; j++) {
            printf("B[%d][%d] = ", i, j);
            scanf("%d", &B[i][j]);
        }
    }
    
    // ====== MATRIX ADDITION ======
    for(i = 0; i < rows; i++) {
        for(j = 0; j < cols; j++) {
            C[i][j] = A[i][j] + B[i][j];
        }
    }
    
    // ====== DISPLAY MATRICES ======
    printf("\n=== First Matrix (%d×%d) ===\n", rows, cols);
    for(i = 0; i < rows; i++) {
        for(j = 0; j < cols; j++) {
            printf("%d\t", A[i][j]);
        }
        printf("\n");
    }
    
    printf("\n=== Second Matrix (%d×%d) ===\n", rows, cols);
    for(i = 0; i < rows; i++) {
        for(j = 0; j < cols; j++) {
            printf("%d\t", B[i][j]);
        }
        printf("\n");
    }
    
    printf("\n=== Result Matrix (%d×%d) ===\n", rows, cols);
    for(i = 0; i < rows; i++) {
        for(j = 0; j < cols; j++) {
            printf("%d\t", C[i][j]);
        }
        printf("\n");
    }
    
    return 0;
}

Sample Output

Enter the number of rows: 2
Enter the number of columns: 3

Enter 6 elements for first matrix:
A[0][0] = 1
A[0][1] = 2
A[0][2] = 3
A[1][0] = 4
A[1][1] = 5
A[1][2] = 6

Enter 6 elements for second matrix:
B[0][0] = 7
B[0][1] = 8
B[0][2] = 9
B[1][0] = 10
B[1][1] = 11
B[1][2] = 12

=== First Matrix (2×3) ===
1	2	3
4	5	6

=== Second Matrix (2×3) ===
7	8	9
10	11	12

=== Result Matrix (2×3) ===
8	10	12
14	16	18

Example with Square Matrices:

Enter the number of rows: 3
Enter the number of columns: 3

Enter 9 elements for first matrix:
A[0][0] = 1
A[0][1] = 2
A[0][2] = 3
A[1][0] = 4
A[1][1] = 5
A[1][2] = 6
A[2][0] = 7
A[2][1] = 8
A[2][2] = 9

Enter 9 elements for second matrix:
B[0][0] = 9
B[0][1] = 8
B[0][2] = 7
B[1][0] = 6
B[1][1] = 5
B[1][2] = 4
B[2][0] = 3
B[2][1] = 2
B[2][2] = 1

=== First Matrix (3×3) ===
1	2	3
4	5	6
7	8	9

=== Second Matrix (3×3) ===
9	8	7
6	5	4
3	2	1

=== Result Matrix (3×3) ===
10	10	10
10	10	10
10	10	10

Program Explanation

Let's break down the code step by step:

Include Header File: #include <stdio.h> includes the standard input/output library.
Declare Variables:
- int rows, cols; — dimensions of the matrices
- int i, j; — loop counters
Declare Matrices:
- int A[rows][cols]; — first matrix
- int B[rows][cols]; — second matrix
- int C[rows][cols]; — result matrix
Read Matrices: Uses nested loops to read elements into both matrices.
Matrix Addition: The nested loops add corresponding elements and store the result in C[i][j].
Display Matrices: Prints all three matrices.
Return: return 0; indicates successful program execution.

📝 Note: The matrices must have the same dimensions for addition to work. If the dimensions differ, the program will not produce correct results.

Algorithm for Matrix Addition

Step-by-step algorithm:

Start
Read the number of rows and columns
Read elements of first matrix (A)
Read elements of second matrix (B)
For i = 0 to rows-1:
- For j = 0 to cols-1:
  - C[i][j] = A[i][j] + B[i][j]
Print the result matrix
End

Adding Matrices with Dimension Validation

A more robust program checks if the matrices have the same dimensions before performing addition:

#include <stdio.h>

int main() {
    int r1, c1, r2, c2, i, j;
    
    printf("Enter rows and columns of first matrix: ");
    scanf("%d %d", &r1, &c1);
    printf("Enter rows and columns of second matrix: ");
    scanf("%d %d", &r2, &c2);
    
    // Check if addition is possible
    if(r1 != r2 || c1 != c2) {
        printf("\n❌ Matrix addition not possible!\n");
        printf("Both matrices must have the same dimensions.\n");
        return 1;
    }
    
    int A[r1][c1], B[r2][c2], C[r1][c1];
    
    // Read matrices (code omitted for brevity)
    // ... read A and B
    
    // Add matrices
    for(i = 0; i < r1; i++) {
        for(j = 0; j < c1; j++) {
            C[i][j] = A[i][j] + B[i][j];
        }
    }
    
    // Display result
    printf("\n=== Result Matrix ===\n");
    for(i = 0; i < r1; i++) {
        for(j = 0; j < c1; j++) {
            printf("%d\t", C[i][j]);
        }
        printf("\n");
    }
    
    return 0;
}

Sample Output (Error Case):

Enter rows and columns of first matrix: 2 3
Enter rows and columns of second matrix: 2 4

❌ Matrix addition not possible!
Both matrices must have the same dimensions.

Time and Space Complexity

Operation	Time Complexity	Space Complexity
Reading Matrices	O(r × c)	O(1)
Matrix Addition	O(r × c)	O(1)
Overall	O(r × c)	O(r × c)

💻 Practice Exercise

Challenge 1: Write a program to add two matrices using functions (create a function for matrix addition).

Challenge 2: Add three matrices together.

🔍 Click to Show Solution for Challenge 1

#include <stdio.h>

void addMatrices(int A[][10], int B[][10], int C[][10], int rows, int cols) {
    int i, j;
    for(i = 0; i < rows; i++) {
        for(j = 0; j < cols; j++) {
            C[i][j] = A[i][j] + B[i][j];
        }
    }
}

void displayMatrix(int matrix[][10], int rows, int cols) {
    int i, j;
    for(i = 0; i < rows; i++) {
        for(j = 0; j < cols; j++) {
            printf("%d\t", matrix[i][j]);
        }
        printf("\n");
    }
}

int main() {
    int rows, cols;
    
    printf("Enter rows and columns: ");
    scanf("%d %d", &rows, &cols);
    
    int A[10][10], B[10][10], C[10][10];
    
    printf("\nEnter elements of first matrix:\n");
    for(int i = 0; i < rows; i++) {
        for(int j = 0; j < cols; j++) {
            scanf("%d", &A[i][j]);
        }
    }
    
    printf("\nEnter elements of second matrix:\n");
    for(int i = 0; i < rows; i++) {
        for(int j = 0; j < cols; j++) {
            scanf("%d", &B[i][j]);
        }
    }
    
    addMatrices(A, B, C, rows, cols);
    
    printf("\nResult Matrix:\n");
    displayMatrix(C, rows, cols);
    
    return 0;
}

Frequently Asked Questions

1. What is the condition for matrix addition?

Both matrices must have the same dimensions (same number of rows and columns). If A is m × n, then B must also be m × n.

2. How do you add two matrices in C?

Use nested loops to iterate through each element and add corresponding elements: C[i][j] = A[i][j] + B[i][j].

3. What is the time complexity of matrix addition?

The time complexity is O(r × c), where r is the number of rows and c is the number of columns.

4. Is matrix addition commutative?

Yes, matrix addition is commutative. A + B = B + A. It is also associative: (A + B) + C = A + (B + C).

5. Can we add a matrix to itself?

Yes, adding a matrix to itself is the same as multiplying it by 2. For example, A + A = 2A.

💡 Tip: Always check that the matrices have the same dimensions before performing addition. Otherwise, the operation is not defined.

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