C program to check if matrix is ​​antisymmetric?

If for all i and j, the elements of the square matrix A satisfy aij=−aji, then the square matrix A is called an antisymmetric matrix. In other words, if the transpose of matrix A is equal to the negative value of matrix A, that is, (A^T=−A), then matrix A is called an antisymmetric matrix.

Note that all main diagonal elements of an antisymmetric matrix are zero.

Let us take an example of a matrix

A= |0 -5 4|
   |5 0 -1|
   |-4 1 0|

This is a skew symmetric matrix because for all i and j, aij=−aji. For example, a12 = -5, a21 = 5, which means a12 = −a21. Likewise, this condition holds for all other values ​​of i and j.

We can also verify that the transpose of matrix A is equal to the negative number of matrix A, that is, A^T=−A.

A<sup>T</sup>= |0 5 -4|
    |-5 0 1|
    |4 -1 0|
and
A= |0 -5 4|
   |5 0 -1|
   |-4 1 0|

We can clearly see that AT=−A, which makes A a skew symmetric matrix.

Input:
Enter the number of rows and columns: 2 2
Enter the matrix elements: 10 20 20 10
Output:
The matrix is symmetric.
10 20
20 10

Explanation

A matrix is ​​a symmetric matrix if it is equal to its transpose.

Otherwise, if its transpose is equal to its negative, then the matrix is ​​antisymmetric. Otherwise it is neither symmetric nor antisymmetric. The results will be printed accordingly.

The process for checking matrix symmetry is as follows:

• Requires the user to enter the number of rows and columns of the matrix.

• Requires the elements of the input matrix and stores them in 'A'. Initialize the variables 'x' and 'y' to 0.

• If the matrix is ​​not equal to its transpose, assign the value of 1 to the temporary variable 'x'.

• Otherwise, if the negative number of the matrix is ​​equal to its transpose, assign the value of 1 to the temporary variable 'y'.

• If x equals 0, the matrix is ​​symmetric. Otherwise, if y equals 1, the matrix is ​​antisymmetric.

• If none of the above conditions are met, the matrix is ​​neither symmetric nor antisymmetric.

• Then print the result.

Example

#include<iostream>
using namespace std;
int main () {
   int A[10][10], i, j, m, n, x = 0, y = 0;
   cout << "Enter the number of rows and columns : ";
   cin >> m >> n;
   cout << "Enter the matrix elements : ";
   for (i = 0; i < m; i++)
      for (j = 0; j < n; j++)
   cin >> A[i][j];
   for (i = 0; i < m; i++) {
      for( j = 0; j < n; j++) {
         if (A[i][j] != A[j][i])
            x = 1;
         else if (A[i][j] == -A[j][i])
            y = 1;
      }
   }
   if (x == 0)
      cout << "The matrix is symmetric.</p><p> ";
   else if (y == 1)
      cout << "The matrix is skew symmetric.</p><p> ";
   else
      cout << "It is neither symmetric nor skew-symmetric.</p><p> ";
   for (i = 0; i < m; i++) {
      for (j = 0; j < n; j++)
         cout << A[i][j] << " ";
      cout << "</p><p> ";
   }
   return 0;
}

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