How to multiply two matrices using pointers in C?

Matrix multiplication is a fundamental operation in linear algebra. In C programming, we can multiply two matrices using pointers to access matrix elements efficiently. This approach demonstrates how pointer arithmetic works with 2D arrays.

Syntax

// Matrix multiplication using pointers
*(*(result + i) + j) = sum of (*(*(mat1 + i) + k)) * (*(*(mat2 + k) + j))

Understanding Pointer Access in 2D Arrays

When working with 2D arrays and pointers −

• mat[i][j] is equivalent to *(*(mat + i) + j)
• mat + i points to the i-th row
• *(mat + i) gives the address of the first element in i-th row
• *(mat + i) + j points to the j-th element in i-th row
• *(*(mat + i) + j) gives the value at mat[i][j]

Example: Matrix Multiplication Using Pointers

Here's a complete program that multiplies two 3x3 matrices using pointer notation −

#include <stdio.h>
#define ROW 3
#define COL 3

/* Function declarations */
void matrixInput(int mat[][COL]);
void matrixPrint(int mat[][COL]);
void matrixMultiply(int mat1[][COL], int mat2[][COL], int res[][COL]);

int main() {
    int mat1[ROW][COL] = {{2, 3, 1}, {2, 5, 6}, {2, 6, 8}};
    int mat2[ROW][COL] = {{1, 2, 1}, {2, 3, 4}, {5, 6, 7}};
    int product[ROW][COL];
    
    printf("First matrix:<br>");
    matrixPrint(mat1);
    
    printf("\nSecond matrix:<br>");
    matrixPrint(mat2);
    
    matrixMultiply(mat1, mat2, product);
    
    printf("\nProduct of both matrices:<br>");
    matrixPrint(product);
    
    return 0;
}

void matrixPrint(int mat[][COL]) {
    int row, col;
    for (row = 0; row < ROW; row++) {
        for (col = 0; col < COL; col++) {
            printf("%d ", *(*(mat + row) + col));
        }
        printf("<br>");
    }
}

void matrixMultiply(int mat1[][COL], int mat2[][COL], int res[][COL]) {
    int row, col, i;
    int sum;
    
    for (row = 0; row < ROW; row++) {
        for (col = 0; col < COL; col++) {
            sum = 0;
            for (i = 0; i < COL; i++) {
                sum += (*(*(mat1 + row) + i)) * (*(*(mat2 + i) + col));
            }
            *(*(res + row) + col) = sum;
        }
    }
}

First matrix:
2 3 1 
2 5 6 
2 6 8 

Second matrix:
1 2 1 
2 3 4 
5 6 7 

Product of both matrices:
13 19 21 
42 55 64 
54 70 82 

How Matrix Multiplication Works

The multiplication follows this formula for each element −

result[i][j] = sum of (mat1[i][k] * mat2[k][j]) for k = 0 to COL-1

Using pointer notation −

*(*(res + i) + j) = sum of (*(*(mat1 + i) + k)) * (*(*(mat2 + k) + j))

Key Points

• Matrix multiplication requires the number of columns in the first matrix to equal the number of rows in the second matrix
• Pointer arithmetic *(*(mat + row) + col) is equivalent to mat[row][col]
• The nested loops iterate through rows, columns, and perform dot product calculation
• Time complexity is O(n³) for n×n matrices

Conclusion

Matrix multiplication using pointers in C demonstrates advanced pointer arithmetic with 2D arrays. This approach provides direct memory access and helps understand how arrays are stored and accessed in memory.