Check Involuntary Matrix

Check Involuntary Matrix” is a problem of matrix where we need to check whether given matrix is an involuntary matrix or not.

There are basically three different types of matrix:

  1. Identity Matrix: An identity matrix is a square matrix of size N*N which have all the diagonal element as 1 and others as 0.
  2. Idempotent Matrix: An Idempotent matrix is a matrix which is when multiplied by itself produces the same matrix.
  3. Involuntary Matrix: An involutory matrix is a matrix which when multiplied by itself gives identity matrix.

Here, we are given a square matrix of size N*N. Our task is to check whether the given matrix is involuntary matrix or not. 

Example:

INPUT:
N=3
1  0  0
0 -1  0
0  0 -1
OUTPUT:
Involutory Matrix!!

The solution of the above problem is to multiply the given matrix by itself and store the result in resultant matrix. If the resultant matrix identity matrix, then given matrix is said to be involutory matrix. Else, it is not an involutory matrix.


C++ Program to check whether given matrix is involutory matrix or not is as follows:

#include<bits/stdc++.h>  
using namespace std;  
int main() 
{  
    // Scan Dimension of the matrix  
    int n;  
    cout<<"Enter the dimesion of square matrix:\n";  
    cin>>n;  
      
    // Scan Elements of the matrix  
    int matrix[n][n];  
    cout<<"Enter the elements of square matrix:\n";  
    for(int i = 0 ; i < n ; i++)  
    for(int j = 0 ; j < n ; j++)  
    cin>>matrix[i][j];  
      
    // Initializing resultant matrix with 0  
    int resultant[n][n];  
    for(int i = 0 ; i < n ; i++)  
    for(int j = 0 ; j < n ; j++)  
    resultant[i][j] = 0;  
      
    //Multiply the matrix with itself and storing  
    // the result in resultant matrix  
    for (int i = 0 ; i < n ; i++)  
    {  
        for (int j = 0 ; j < n ; j++)  
        {  
            for (int k = 0 ; k < n ; k++)   
            {  
                resultant[i][j] += matrix[i][k] * matrix[k][j];   
            }  
        }  
    }  
      
    //Check whether the resultant matrix is   
    // involuntary matrix or not   
    bool result = true;  
    for (int i = 0 ; i < n ; i++)  
    {  
        for (int j = 0 ; j < n ; j++)  
        {  
            if(i==j && resultant[i][j]!=1)  
            {  
                result = false;  
                break;  
            }  
            else if(i!=j && resultant[i][j]!=0)  
            {  
                result = false;  
                break;  
            }  
        }  
        if(!result)  
        break;  
    }  
    if(result)  
    cout<<"Involutory Matrix!!";  
    else  
    cout<<"Not Involutory Matrix";  
}  

OUTPUT:
Enter the dimesion of square matrix: 3
Enter the elements of square matrix:
1 0 0 
0 -1 0
0 0 -1
Involutory Matrix!!

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