Read, Display and Trace of a Square Matrix in C

Algorithm

1. Read n and reject values outside 1 to 10.
2. Read the n x n matrix row by row.
3. Print the matrix, one row per line.
4. Add the element a[i][i] for every i from 0 to n - 1 to get the trace.

C program

#include <stdio.h>

#define MAX 10

int main(void) {
    int matrix[MAX][MAX];
    int n, i, j, trace = 0;

    printf("Enter the size n of the square matrix (1-%d):\n", MAX);
    if (scanf("%d", &n) != 1 || n < 1 || n > MAX) {
        printf("Error: size must be from 1 to %d\n", MAX);
        return 1;
    }

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

    printf("Matrix:\n");
    for (i = 0; i < n; i++) {
        for (j = 0; j < n; j++) {
            printf("%4d", matrix[i][j]);
        }
        printf("\n");
    }

    for (i = 0; i < n; i++) {
        trace += matrix[i][i];
    }
    printf("Trace: %d\n", trace);
    return 0;
}

Sample input and output

3
1 2 3
4 5 6
7 8 9

Enter the size n of the square matrix (1-10):
Enter the 3 x 3 matrix:
Matrix:
   1   2   3
   4   5   6
   7   8   9
Trace: 15

1
42

Enter the size n of the square matrix (1-10):
Enter the 1 x 1 matrix:
Matrix:
  42
Trace: 42

How the program works

A square matrix has the same number of rows and columns, so the main diagonal is the set of positions where the row index equals the column index. The trace is the sum of exactly those positions.

The trace is defined only for square matrices, which is why the program asks for one size n and reads an n x n block.

Viva questions

Common mistakes

• Summing a[i][j] over all cells instead of only the diagonal.
• Reading a non-square block by using different row and column sizes.