Write a program to multiply two matrices.

Learn how to multiply two matrices in C programming

matrix_multiplication.c

#include <stdio.h>

int main() {
    int A[10][10], B[10][10], C[10][10];
    int r1, c1, r2, c2, i, j, k;

    // Input dimensions of matrix A
    printf("Enter rows and columns for matrix A: ");
    scanf("%d%d", &r1, &c1);

    // Input dimensions of matrix B
    printf("Enter rows and columns for matrix B: ");
    scanf("%d%d", &r2, &c2);

    // Check multiplication condition
    if(c1 != r2) {
        printf("Matrix multiplication not possible. Columns of A must equal rows of B.\n");
        return 0;
    }

    // Input elements of matrix A
    printf("Enter elements of matrix A:\n");
    for(i = 0; i < r1; i++) {
        for(j = 0; j < c1; j++) {
            printf("A[%d][%d]: ", i, j);
            scanf("%d", &A[i][j]);
        }
    }

    // Input elements of matrix B
    printf("Enter elements of matrix B:\n");
    for(i = 0; i < r2; i++) {
        for(j = 0; j < c2; j++) {
            printf("B[%d][%d]: ", i, j);
            scanf("%d", &B[i][j]);
        }
    }

    // Multiply matrices
    for(i = 0; i < r1; i++) {
        for(j = 0; j < c2; j++) {
            C[i][j] = 0;
            for(k = 0; k < c1; k++) {
                C[i][j] += A[i][k] * B[k][j];
            }
        }
    }

    // Display result matrix
    printf("\nResultant Matrix C (A x B):\n");
    for(i = 0; i < r1; i++) {
        for(j = 0; j < c2; j++) {
            printf("%d\t", C[i][j]);
        }
        printf("\n");
    }

    return 0;
}

🧾 Step-by-Step Explanation

🔹 Step 1: Include Header File

#include <stdio.h>

This standard library provides essential functions:

• printf() for displaying output
• scanf() for reading user input
• Basic console I/O operations

🔹 Step 2: Declare Matrices and Variables

int A[10][10], B[10][10], C[10][10];
int r1, c1, r2, c2, i, j, k;

• A, B, C: 10×10 matrices (2D arrays)
• r1, c1: Rows and columns of Matrix A
• r2, c2: Rows and columns of Matrix B
• i, j, k: Loop counters for matrix operations

🔹 Step 3: Input Matrix Dimensions

printf("Enter rows and columns for matrix A: ");
scanf("%d%d", &r1, &c1);

printf("Enter rows and columns for matrix B: ");
scanf("%d%d", &r2, &c2);

• Gets dimensions for both matrices from user
• Uses %d%d to read two integers at once
• Maximum size is 10×10 as declared

🔹 Step 4: Check Multiplication Condition

if(c1 != r2) {
    printf("Matrix multiplication not possible.\n");
    return 0;
}

• Verifies columns of A match rows of B
• Matrix multiplication requires this condition
• Exits program if condition fails

🔹 Step 5: Input Matrix Elements

for(i = 0; i < r1; i++) {
    for(j = 0; j < c1; j++) {
        scanf("%d", &A[i][j]);
    }
}

• Nested loops to read each matrix element
• First for rows, second for columns
• Same process for both matrices A and B
• Displays position with each input prompt

🔹 Step 6: Multiply Matrices

for(i = 0; i < r1; i++) {
    for(j = 0; j < c2; j++) {
        C[i][j] = 0;
        for(k = 0; k < c1; k++) {
            C[i][j] += A[i][k] * B[k][j];
        }
    }
}

Matrix multiplication algorithm:

• Outer loops: Iterate through result matrix positions
• Inner loop: Computes dot product of row from A and column from B
• Initialization: Sets result position to 0 before accumulation
• Accumulation: Sums products of corresponding elements

🔹 Step 7: Display Result Matrix

for(i = 0; i < r1; i++) {
    for(j = 0; j < c2; j++) {
        printf("%d\t", C[i][j]);
    }
    printf("\n");
}

• Prints result matrix in tabular format
• Uses \t for column alignment
• Uses \n after each row
• Shows final product of matrix multiplication

🧪 Sample Output

Enter rows and columns for matrix A: 2 3
Enter rows and columns for matrix B: 3 2
Enter elements of matrix A:
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 elements of matrix B:
B[0][0]: 7
B[0][1]: 8
B[1][0]: 9
B[1][1]: 10
B[2][0]: 11
B[2][1]: 12

Resultant Matrix C (A x B):
58      64
139     154

📌 Key Concepts Covered

Matrix Multiplication

Dot product of rows from first matrix with columns from second matrix

2D Arrays

Used to represent matrices with rows and columns

Triple Nested Loops

Outer two for result matrix positions, inner for multiplication/summation

Dimension Validation

Ensures columns of first matrix match rows of second matrix

Tabular Output

Formatted display of matrix with rows and columns properly aligned