How to multiply two 2D matrices in C

Matrix Multiplication in C for Absolute Beginners

Introduction

In this post, we will learn how to multiply two matrices in C programming. Matrix multiplication is an important concept in mathematics and computer science, used in data analysis, machine learning, and various other fields. We’ll break down the code step-by-step, making it easy for beginners to understand.

Understanding Matrix Multiplication

Matrix multiplication differs from simple element-wise addition. For matrix multiplication:

  • If we have two matrices, Matrix A (of dimensions m x n) and Matrix B (of dimensions n x p), we can multiply them to get a resultant Matrix C (of dimensions m x p).
  • Each element in the resultant matrix is obtained by taking the dot product of the rows of Matrix A and the columns of Matrix B.

Here’s an example to visualize it:

Matrix A:      Matrix B:         Result Matrix C:
2 4            1 2 3             (2*1 + 4*4)  (2*2 + 4*5)  (2*3 + 4*6)
3 5            4 5 6             (3*1 + 5*4)  (3*2 + 5*5)  (3*3 + 5*6)

Steps for Matrix Multiplication

  1. Ensure the number of columns in Matrix A is equal to the number of rows in Matrix B.
  2. For each element in the result matrix, take the corresponding row from Matrix A and the column from Matrix B, multiply each pair of elements, and sum them.

Let’s see how to write this in a C program.

Matrix Multiplication Code in C

#include <stdio.h>

int main() {
    int rowsA, colsA, rowsB, colsB;

    // Step 1: Get matrix dimensions
    printf("Enter the number of rows and columns of Matrix A: ");
    scanf("%d %d", &rowsA, &colsA);

    printf("Enter the number of rows and columns of Matrix B: ");
    scanf("%d %d", &rowsB, &colsB);

    // Check if multiplication is possible
    if (colsA != rowsB) {
        printf("Matrix multiplication not possible. Columns of A must equal rows of B.\n");
        return 0;
    }

    int matrixA[rowsA][colsA], matrixB[rowsB][colsB], result[rowsA][colsB];

    // Initialize result matrix to zero
    for (int i = 0; i < rowsA; i++) {
        for (int j = 0; j < colsB; j++) {
            result[i][j] = 0;
        }
    }

    // Step 2: Input elements for Matrix A
    printf("Enter elements of Matrix A:\n");
    for (int i = 0; i < rowsA; i++) {
        for (int j = 0; j < colsA; j++) {
            printf("Enter element at position (%d, %d): ", i + 1, j + 1);
            scanf("%d", &matrixA[i][j]);
        }
    }

    // Step 3: Input elements for Matrix B
    printf("Enter elements of Matrix B:\n");
    for (int i = 0; i < rowsB; i++) {
        for (int j = 0; j < colsB; j++) {
            printf("Enter element at position (%d, %d): ", i + 1, j + 1);
            scanf("%d", &matrixB[i][j]);
        }
    }

    // Step 4: Multiply matrices
    for (int i = 0; i < rowsA; i++) {
        for (int j = 0; j < colsB; j++) {
            for (int k = 0; k < colsA; k++) {
                result[i][j] += matrixA[i][k] * matrixB[k][j];
            }
        }
    }

    // Step 5: Display the result matrix
    printf("Resultant Matrix after multiplication:\n");
    for (int i = 0; i < rowsA; i++) {
        for (int j = 0; j < colsB; j++) {
            printf("%d ", result[i][j]);
        }
        printf("\n");
    }

    return 0;
}

Explanation of Code, Line by Line

Let’s go through each part of this program to understand how it works.

1. Including the Standard I/O Library

#include <stdio.h>
  • This line includes the standard input-output library, allowing us to use functions like printf and scanf.

2. Declaring main Function

int main() {
  • Here, we start the main function, where the program’s execution begins.

3. Declaring Variables for Rows and Columns

int rowsA, colsA, rowsB, colsB;
  • We declare variables to store the number of rows and columns for both matrices.

4. Taking Matrix Dimensions from the User

printf("Enter the number of rows and columns of Matrix A: ");
scanf("%d %d", &rowsA, &colsA);
printf("Enter the number of rows and columns of Matrix B: ");
scanf("%d %d", &rowsB, &colsB);
  • We ask the user to input the dimensions of Matrix A and Matrix B.

5. Check if Multiplication is Possible

if (colsA != rowsB) {
    printf("Matrix multiplication not possible. Columns of A must equal rows of B.\n");
    return 0;
}
  • We check if the number of columns in Matrix A is equal to the number of rows in Matrix B. If not, matrix multiplication cannot be done, and we end the program.

6. Declaring Matrices

int matrixA[rowsA][colsA], matrixB[rowsB][colsB], result[rowsA][colsB];
  • We declare arrays for Matrix A, Matrix B, and the resultant matrix.

7. Initializing the Result Matrix to Zero

for (int i = 0; i < rowsA; i++) {
    for (int j = 0; j < colsB; j++) {
        result[i][j] = 0;
    }
}
  • We initialize all elements in the result matrix to zero since we will add values to it during multiplication.

8. Taking Input for Matrix A

printf("Enter elements of Matrix A:\n");
for (int i = 0; i < rowsA; i++) {
    for (int j = 0; j < colsA; j++) {
        printf("Enter element at position (%d, %d): ", i + 1, j + 1);
        scanf("%d", &matrixA[i][j]);
    }
}
  • We take input for each element of Matrix A from the user.

9. Taking Input for Matrix B

printf("Enter elements of Matrix B:\n");
for (int i = 0; i < rowsB; i++) {
    for (int j = 0; j < colsB; j++) {
        printf("Enter element at position (%d, %d): ", i + 1, j + 1);
        scanf("%d", &matrixB[i][j]);
    }
}
  • This block is similar to Step 8 but for Matrix B.

10. Performing Matrix Multiplication

for (int i = 0; i < rowsA; i++) {
    for (int j = 0; j < colsB; j++) {
        for (int k = 0; k < colsA; k++) {
            result[i][j] += matrixA[i][k] * matrixB[k][j];
        }
    }
}
  • This is the main part of the code where we perform matrix multiplication.
  • For each element in the result matrix, we multiply elements in a row from Matrix A with elements in a column from Matrix B, and then sum them up.

11. Displaying the Result Matrix

printf("Resultant Matrix after multiplication:\n");
for (int i = 0; i < rowsA; i++) {
    for (int j = 0; j < colsB; j++) {
        printf("%d ", result[i][j]);
    }
    printf("\n");
}
  • Finally, we print the resultant matrix by iterating through each row and column of the result matrix.

12. Ending the Program

return 0;
}
  • This return 0; statement signals that the program finished successfully.

Example Output

Suppose the user enters the following matrices:

Matrix A:             Matrix B:
2 3                   1 2
4 5                   3 4

The result after multiplication will be:

Resultant Matrix:
11 16
19 28

Conclusion

Matrix multiplication in C may look complex initially, but with a structured approach, it becomes easier to implement. This program introduces the concept of nested loops and array manipulation, making it ideal for beginners interested in learning about matrix

operations.

Feel free to modify and try with larger matrices! Happy coding!

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