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C Program to multiply two matrix.

C Code Example — Array Programs

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C Program to multiply two matrix.

Objective

Write a C program to multiply two matrices.

Algorithm / Approach

  1. Declare m1 as 3x2, m2 as 2x4, and the result m3 as 3x4.
  2. Read the data for m1 and m2.
  3. Use THREE nested loops (i for M1 rows, j for M2 cols, k for the common inner dimension).
  4. Calculate the dot product for each cell: sum = sum + m1[i][k] * m2[k][j].
  5. Assign the sum to m3[i][j] and reset sum = 0.
  6. Print the final product matrix.
main.c 
#include<stdio.h>
int main( ) {
 int r1=3, c1=2, r2=2, c2=4;
 int i, j, k, sum = 0;
 int m1[3][2], m2[2][4], m3[3][4];
 printf("Enter elements of mat1: "); 
 for (i = 0; i < r1; i++){
   for (j = 0; j < c1; j++){
     scanf("%d", &m1[i][j]);
   }
 }
 printf("Enter elements mat2: ");
 for (i = 0; i < r2; i++){
  for (j = 0; j < c2; j++){
    scanf("%d", &m2[i][j]);
  }
 }
 
for (i=0; i < r1; i++){
  for (j=0; j < c2; j++){
    for (k=0; k < r2; k++){
      sum = sum + m1[i][k]*m2[k][j];
    }
    m3[i][j] = sum;
    sum = 0;
  }
}
printf("Product of Matrix : \n");
for (i=0; i < r1; i++) {
  for (j=0; j < c2; j++){
    printf("%d  ", m3[i][j]);
   }
   printf("\n");
  }
 return 0;
}

Expected Output

Enter elements of mat1 : 
1 3
3 4
2 3
Enter elements of mat2 :
1 2 3 4
3 4 5 6
Product of Matrix :
10  14  18  22
15  22  29  36
11  16  21  26

Explanation of the Program

  • Matrix multiplication is much more complex than addition. You must calculate the "dot product" of the rows of the first matrix against the columns of the second matrix.
  • Rule of Matrix Multiplication: The number of columns in the first matrix MUST equal the number of rows in the second matrix. (e.g., a 3x2 matrix can multiply a 2x4 matrix, resulting in a 3x4 matrix).
  • This requires three nested loops: two to traverse the resulting matrix grid, and a third (k) to calculate the sliding dot product.

Complexity

Time Complexity O(r1 * c2 * r2) - Cubic time complexity.
Space Complexity O(r1 * c2) - To store the resulting matrix.
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