Matrix Multiplication with Validation in C

Algorithm

1. Read the dimensions r1 x c1 of matrix A and r2 x c2 of matrix B, each up to 10.
2. If c1 is not equal to r2, print that multiplication is not possible and stop.
3. Read matrix A and matrix B.
4. For each cell (i, j) of the r1 x c2 result, sum A[i][k] * B[k][j] over k from 0 to c1 - 1.
5. Print the result matrix row by row.

C program

#include <stdio.h>

#define MAX 10

int main(void) {
    int a[MAX][MAX], b[MAX][MAX], c[MAX][MAX];
    int r1, c1, r2, c2, i, j, k, sum;

    printf("Enter rows and columns of matrix A:\n");
    scanf("%d %d", &r1, &c1);
    printf("Enter rows and columns of matrix B:\n");
    scanf("%d %d", &r2, &c2);

    if (r1 < 1 || c1 < 1 || r2 < 1 || c2 < 1 || r1 > MAX || c1 > MAX || r2 > MAX || c2 > MAX) {
        printf("Error: each dimension must be between 1 and %d\n", MAX);
        return 1;
    }

    if (c1 != r2) {
        printf("Error: cannot multiply a %dx%d matrix by a %dx%d matrix (%d columns vs %d rows)\n",
               r1, c1, r2, c2, c1, r2);
        return 1;
    }

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

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

    for (i = 0; i < r1; i++) {
        for (j = 0; j < c2; j++) {
            sum = 0;
            for (k = 0; k < c1; k++) {
                sum += a[i][k] * b[k][j];
            }
            c[i][j] = sum;
        }
    }

    printf("Product matrix:\n");
    for (i = 0; i < r1; i++) {
        for (j = 0; j < c2; j++) {
            printf("%d ", c[i][j]);
        }
        printf("\n");
    }
    return 0;
}

Sample input and output

2 3
3 2
1 2 3
4 5 6
7 8
9 10
11 12

Enter rows and columns of matrix A:
Enter rows and columns of matrix B:
Enter matrix A:
Enter matrix B:
Product matrix:
58 64 
139 154

2 3
2 2

Enter rows and columns of matrix A:
Enter rows and columns of matrix B:
Error: cannot multiply a 2x3 matrix by a 2x2 matrix (3 columns vs 2 rows)

How the program works

The rule is checked before any element is read, because the result would otherwise be undefined. A matrix with r1 rows and c1 columns times one with r2 rows and c2 columns is defined only when c1 = r2, and the result then has r1 rows and c2 columns.

Each result cell is the dot product of a row of A with a column of B. The three nested loops follow that definition directly: i and j pick the cell and k walks along the shared dimension.

Viva questions

Common mistakes

• Skipping the c1 = r2 check, which reads and multiplies out-of-range data.
• Forgetting to reset sum for each cell, so values accumulate across cells.
• Swapping the loop bounds so that the result has the wrong shape.