Mathematical Principle

Matrix multiplication between matrix A (of dimensions R1 × C1) and matrix B (of dimensions R2 × C2) is possible if and only if the number of columns in A equals the number of rows in B (C1 = R2).

The resulting product matrix C has dimensions $R_1 × C_2$, where each cell is calculated as:

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C[i][j] = ∑ (A[i][k] × B[k][j]) for k = 0 to C1 - 1

Complete C Implementation

c (ISO Standard)
Run in Compiler.cCopy
#include <stdio.h>

#define R1 2
#define C1 3
#define R2 3
#define C2 2

void multiplyMatrices(int a[R1][C1], int b[R2][C2], int result[R1][C2]) {
    /* Initialize all elements of result matrix to 0 */
    for (int i = 0; i < R1; i++) {
        for (int j = 0; j < C2; j++) {
            result[i][j] = 0;
        }
    }

    /* Triple nested loop to calculate dot products */
    for (int i = 0; i < R1; i++) {
        for (int j = 0; j < C2; j++) {
            for (int k = 0; k < C1; k++) {
                result[i][j] += a[i][k] * b[k][j];
            }
        }
    }
}

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

int main() {
    int matA[R1][C1] = {
        {1, 2, 3},
        {4, 5, 6}
    };

    int matB[R2][C2] = {
        {7, 8},
        {9, 1},
        {2, 3}
    };

    int product[R1][C2];

    multiplyMatrices(matA, matB, product);

    printf("Matrix A (%dx%d):\n", R1, C1);
    printMatrix(R1, C1, matA);

    printf("\nMatrix B (%dx%d):\n", R2, C2);
    printMatrix(R2, C2, matB);

    printf("\nResultant Product Matrix (%dx%d):\n", R1, C2);
    printMatrix(R1, C2, product);

    return 0;
}

Expected Output

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Matrix A (2x3):
1	2	3	
4	5	6	

Matrix B (3x2):
7	8	
9	1	
2	3	

Resultant Product Matrix (2x2):
31	19	
85	55	

Complexity Analysis

• Time Complexity: O(R1 × C2 × C1) ≈ O(n³) for $n × n$ square matrices.
• Space Complexity: O(R1 × C2) auxiliary space for the output matrix.

Related Tutorials

• Learn how multidimensional memory is laid out in Arrays in C Programming.
• Practice pointer-based algorithms with Bubble Sort in C.