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. 


1 0 0 0 
0 1 0 0
0 0 1 0 
0 0 0 1

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

/* Program to check Identity Matrix */
using namespace std;  
int main()  
    int N;  
    // Scan Dimensions of the matrix  
    cout<<"Enter the dimension of the matrix:\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++)  
    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;  
            else if(i!=j && matrix[i][j]!=0)  
                result = false;  
    // Print the result  
    cout<<"The Matrix is Identity Matrix";  
    cout<<"The Matrix is not Identity Matrix";  

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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