Check Identity Matrix

“Check Identity Matrix” is a problem of matrix where we need to check whether given matrix is an identity 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 identity matrix or not. 

Example:

INPUT:
1 0 0 0 
0 1 0 0
0 0 1 0 
0 0 0 1
OUTPUT:
TRUE

C++ Program to check Identity Matrix is as follows:

#include<bits/stdc++.h>  
using namespace std;  
int main()  
{  
    int N;  
    // Scan Dimensions of the matrix  
    cout<<"Enter the dimension of the matrix:\n";  
    cin>>N;  
      
    int matrix[N][N];  
      
    // Scan Matrix Elements  
    cout<<"Enter the elements of the matrix:\n";  
    for(int i = 0 ; i < N ; i++)  
    for(int j = 0 ; j < N ; j++)  
    cin>>matrix[i][j];  
      
    bool result = true;  
      
    // Check Identity matrix  
    for(int i = 0 ; i < N ; i++)  
    {  
        for(int j = 0 ; j < N ; j++)  
        {  
            if(i==j && matrix[i][j]!=1)  
            {  
                result = false;  
                break;  
            }  
            else if(i!=j && matrix[i][j]!=0)  
            {  
                result = false;  
                break;  
            }  
        }  
        if(!result)  
        break;  
    }  
      
    // Print the result  
    if(result)  
    cout<<"The Matrix is Identity Matrix";  
    else  
    cout<<"The Matrix is not Identity Matrix";  
}  

OUTPUT:
Enter the dimension of the matrix: 3
Enter the elements of the matrix:
1 0 0 
0 1 0
0 0 1
The Matrix is Identity Matrix

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