Trust Coding : Programming: Write a C program that takes the dimensions and elements of two matrices A (n × m) and B (m × p) from the user, checks whether multiplication is possible, and prints the resulting matrix C (A × B).Write a C program that takes the dimensions and elements of two matrices A (n × m) and B (m × p) from the user, checks whether multiplication is possible, and prints the resulting matrix C (A × B).

Matrix Multiplication in C (A × B)

In this tutorial, we will write a C program that:

Takes dimensions and elements of two matrices A (n × m) and B (m × p)
Checks whether multiplication is possible
Prints the resulting matrix C (A × B)

Condition for Matrix Multiplication

Matrix multiplication is possible only if:


Number of columns of A = Number of rows of B
(m = m)

If this condition is not satisfied, multiplication is not possible.

C Program


#include <stdio.h>

int main() {
    int n, m, p;
    int i, j, k;

    printf("Enter rows and columns of Matrix A (n m): ");
    scanf("%d %d", &n, &m);

    printf("Enter columns of Matrix B (p): ");
    scanf("%d", &p);

    int A[n][m], B[m][p], C[n][p];

    printf("Enter elements of Matrix A:\n");
    for(i = 0; i < n; i++) {
        for(j = 0; j < m; j++) {
            scanf("%d", &A[i][j]);
        }
    }

    printf("Enter elements of Matrix B:\n");
    for(i = 0; i < m; i++) {
        for(j = 0; j < p; j++) {
            scanf("%d", &B[i][j]);
        }
    }

    // Initialize result matrix C with 0
    for(i = 0; i < n; i++) {
        for(j = 0; j < p; j++) {
            C[i][j] = 0;
        }
    }

    // Matrix multiplication
    for(i = 0; i < n; i++) {
        for(j = 0; j < p; j++) {
            for(k = 0; k < m; k++) {
                C[i][j] += A[i][k] * B[k][j];
            }
        }
    }

    printf("Resultant Matrix C (A x B):\n");
    for(i = 0; i < n; i++) {
        for(j = 0; j < p; j++) {
            printf("%d ", C[i][j]);
        }
        printf("\n");
    }

    return 0;
}

Explanation

1. Input Dimensions

User enters:

n = rows of A
m = columns of A (and rows of B)
p = columns of B

2. Input Matrices

Matrix A is of size (n × m). Matrix B is of size (m × p).

3. Multiplication Logic


C[i][j] += A[i][k] * B[k][j];

Each element of matrix C is calculated as:

C[i][j] = Σ (A[i][k] × B[k][j])

4. Output

The resultant matrix C (n × p) is printed.

Example

Matrix A (2 × 2):
1 2
3 4

Matrix B (2 × 2):
5 6
7 8

Result Matrix:
19 22
43 50

Time Complexity

Three nested loops are used. Therefore, time complexity is O(n × m × p).

Trust Coding : Programming