Multiply Two Matrices in C: Program for Matrix Multiplication

Introduction

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

Matrix multiplication is a binary operation that produces a matrix from two matrices. It is a fundamental operation in linear algebra and is used in many applications.

Matrix Multiplication Rule

• Matrix A: Dimensions r1 × c1
• Matrix B: Dimensions r2 × c2
• Condition: c1 == r2 (columns of A = rows of B)
• Result Matrix C: Dimensions r1 × c2

Visual Example

[1  2  3]
[4  5  6]

[7   8]
[9  10]
[11 12]

[58  64]
[139 154]

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

• Computer Graphics: Transformations (rotation, scaling, translation)
• Machine Learning: Neural networks and data transformations
• Physics: Quantum mechanics and coordinate transformations
• Economics: Input-output analysis

C Program to Multiply Two Matrices

#include <stdio.h>

int main() {
    int r1, c1, r2, c2, i, j, k;
    
    // ====== FIRST MATRIX ======
    printf("Enter the number of rows and columns of first matrix: ");
    scanf("%d %d", &r1, &c1);
    
    // ====== SECOND MATRIX ======
    printf("Enter the number of rows and columns of second matrix: ");
    scanf("%d %d", &r2, &c2);
    
    // Check if multiplication is possible
    if(c1 != r2) {
        printf("\n❌ Matrix multiplication not possible!\n");
        printf("Number of columns of first matrix (%d) must equal number of rows of second matrix (%d).\n", c1, r2);
        return 1;
    }
    
    // Declare matrices
    int A[r1][c1], B[r2][c2], C[r1][c2];
    
    // ====== READ FIRST MATRIX ======
    printf("\nEnter %d elements for first matrix:\n", r1 * c1);
    for(i = 0; i < r1; i++) {
        for(j = 0; j < c1; j++) {
            printf("A[%d][%d] = ", i, j);
            scanf("%d", &A[i][j]);
        }
    }
    
    // ====== READ SECOND MATRIX ======
    printf("\nEnter %d elements for second matrix:\n", r2 * c2);
    for(i = 0; i < r2; i++) {
        for(j = 0; j < c2; j++) {
            printf("B[%d][%d] = ", i, j);
            scanf("%d", &B[i][j]);
        }
    }
    
    // ====== MATRIX MULTIPLICATION ======
    // Initialize result matrix with 0
    for(i = 0; i < r1; i++) {
        for(j = 0; j < c2; j++) {
            C[i][j] = 0;
        }
    }
    
    // Multiply A and B
    for(i = 0; i < r1; i++) {
        for(j = 0; j < c2; j++) {
            for(k = 0; k < c1; k++) {
                C[i][j] += A[i][k] * B[k][j];
            }
        }
    }
    
    // ====== DISPLAY MATRICES ======
    printf("\n=== First Matrix (%d×%d) ===\n", r1, c1);
    for(i = 0; i < r1; i++) {
        for(j = 0; j < c1; j++) {
            printf("%d\t", A[i][j]);
        }
        printf("\n");
    }
    
    printf("\n=== Second Matrix (%d×%d) ===\n", r2, c2);
    for(i = 0; i < r2; i++) {
        for(j = 0; j < c2; j++) {
            printf("%d\t", B[i][j]);
        }
        printf("\n");
    }
    
    printf("\n=== Result Matrix (%d×%d) ===\n", r1, c2);
    for(i = 0; i < r1; i++) {
        for(j = 0; j < c2; j++) {
            printf("%d\t", C[i][j]);
        }
        printf("\n");
    }
    
    return 0;
}

Sample Output

Enter the number of rows and columns of first matrix: 2 3
Enter the number of rows and columns of second matrix: 3 2

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[1][0] = 9
B[1][1] = 10
B[2][0] = 11
B[2][1] = 12

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

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

=== Result Matrix (2×2) ===
58	64
139	154

Square Matrix Example:

Enter the number of rows and columns of first matrix: 3 3
Enter the number of rows and columns of second matrix: 3 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) ===
30	24	18
84	69	54
138	114	90

When Multiplication is Not Possible:

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

❌ Matrix multiplication not possible!
Number of columns of first matrix (3) must equal number of rows of second matrix (4).

Program Explanation

Let's break down the code step by step:

1. Include Header File: #include <stdio.h> includes the standard input/output library.
2. Declare Variables:
   • int r1, c1; — dimensions of first matrix
   • int r2, c2; — dimensions of second matrix
   • int i, j, k; — loop counters
3. Check Multiplication Condition: If c1 != r2, the matrices cannot be multiplied. Display an error message and exit.
4. Read Matrices: Reads elements into both matrices.
5. Initialize Result Matrix: Sets all elements of C to 0.
6. Matrix Multiplication (Triple Nested Loop):
   • Outer Loop (i): Iterates through rows of A
   • Middle Loop (j): Iterates through columns of B
   • Inner Loop (k): Iterates through the common dimension (columns of A / rows of B)
   • C[i][j] += A[i][k] * B[k][j] — calculates the dot product
7. Display Results: Prints all three matrices.
8. Return: return 0; indicates successful program execution.

Algorithm for Matrix Multiplication

Step-by-step algorithm:

1. Start
2. Read dimensions of first matrix (r1, c1)
3. Read dimensions of second matrix (r2, c2)
4. If c1 != r2:
   • Print "Multiplication not possible"
   • Exit
5. Read elements of first matrix (A)
6. Read elements of second matrix (B)
7. Create result matrix C of size r1 × c2
8. For i = 0 to r1-1:
   • For j = 0 to c2-1:
     • Set C[i][j] = 0
     • For k = 0 to c1-1:
       • C[i][j] += A[i][k] * B[k][j]
9. Print the result matrix
10. End

Visualizing Matrix Multiplication

For C[i][j], we take the ith row of A and the jth column of B:

A: [a11  a12  a13]     B: [b11  b12]     C: [c11  c12]
    [a21  a22  a23]         [b21  b22]         [c21  c22]
                            [b31  b32]

c11 = a11*b11 + a12*b21 + a13*b31
c12 = a11*b12 + a12*b22 + a13*b32
c21 = a21*b11 + a22*b21 + a23*b31
c22 = a21*b12 + a22*b22 + a23*b32

Time and Space Complexity

#include <stdio.h>

void multiplyMatrices(int A[][10], int B[][10], int C[][10], int r1, int c1, int c2) {
    int i, j, k;
    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];
            }
        }
    }
}

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 r1, c1, r2, c2;
    
    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);
    
    if(c1 != r2) {
        printf("Multiplication not possible!\n");
        return 1;
    }
    
    int A[10][10], B[10][10], C[10][10];
    
    // Read matrices (code omitted for brevity)
    // ... read A and B
    
    multiplyMatrices(A, B, C, r1, c1, c2);
    
    printf("\nResult Matrix:\n");
    displayMatrix(C, r1, c2);
    
    return 0;
}

Frequently Asked Questions

Previous Topic: -->> Transpose a Matrix in C   ||   Next topic: -->> Matrix Addition in C