//find if an integer matrix is orthogonal, that is A*tr(A)==tr(A)*A=I, 
//for a matrix up to 10x10
//these matrices are the signature matrices and are diagonal matrices
//whose diagonal elements are plus or minus 1 
#include <iostream>
#include <cmath>
using namespace std;

int main()
{   int i,j,k,N;
    int A[10][10], trA[10][10], C[10][10];
    bool flag;
    cout<<"N ";
    cin>>N;
    cout<<"A[][]"<<endl;
    for (i=0; i<N; i++)
      for (j=0; j<N; j++)
        cin>>A[i][j];

    for (i=0; i<N; i++)
      for (j=0; j<N; j++)
        trA[i][j]=A[j][i];
        
    for (i=0; i<N; i++)
      for (j=0; j<N; j++){
        C[i][j]=0;
        for (k=0; k<N; k++) C[i][j]=C[i][j]+A[i][k]*trA[k][j];
        }  

    for (i=0; i<N; i++){
      for (j=0; j<N; j++) cout<<C[i][j]<<" ";
      cout<<endl;
        } 

    flag=true;
    for (i=0; i<N; i++)
      for (j=0; j<N; j++){
        if (i==j && C[i][j]!=1) {flag=false; break;}
        if (i!=j && C[i][j]!=0) {flag=false; break;}
        }        
	
	if (flag) cout<<"orthogonal"<<endl; else cout<<"not orthogonal"<<endl;
       
    system("PAUSE"); 
    return 0;
}