A symmetric matrix is a square matrix that is equal to its transpose. Let A be a symmetric matrix.
Then,
A = A^T

In this program, we need to check whether the given square matrix is symmetric or not. We will follow the steps given below.

• Step 1 – Accepts a square matrix as input
• Step 2 – Create a transpose of a matrix and store it in an array
• Step 3 – Check if input matrix is equal to its transpose or not
  If it is equal, then the input square matrix is symmetric.

Here it goes…

#include
#include

void main(){
 int arr[10][10], arrT[10][10];
 int i,j;
 clrscr();
 printf("Enter the 3x3 matrix:\n");
 for(i=0;i<3;i++)
 {
  for(j=0;j<3;j++)
  {
   printf("Enter the element arr[%d][%d] : ",i,j);
   scanf("%d",&arr[i][j]);
  }
 }
 for(i=0;i<3;i++)
 {
  for(j=0;j<3;j++)
  {
   arrT[j][i] = arr[i][j];
  }
 }

 for(i=0;i<3;i++)
 {
  for(j=0;j<3;j++)
  {
   if(arr[i][j] == arrT[i][j]){
    continue;
   }
   else{
    printf("\nInput matrix is not a symmetric matrix.");
    getch();
    exit(0);
   }
  }
 }
 printf("\nInput matrix is a symmetric matrix");
 getch();
}

Output:

Enter the 3x3 matrix:
Enter the element arr[0][0] : 1
Enter the element arr[0][1] : 2
Enter the element arr[0][2] : 3
Enter the element arr[1][0] : 2
Enter the element arr[1][1] : 4
Enter the element arr[1][2] : -5
Enter the element arr[2][0] : 3
Enter the element arr[2][1] : -5
Enter the element arr[2][2] : 6

Input matrix is a symmetric matrix