Program to check idempotent matrix

Given a N * N matrix and the task is to check matrix is idempotent matrix or not.

Idempotent matrix: A matrix is said to be idempotent matrix if matrix multiplied by itself return the same matrix. The matrix M is said to be idempotent matrix if and only if M * M = M. In idempotent matrix M is a square matrix.

idempotent matrix

Examples:

Input : mat[][] = {{3, -6},
                   {1, -2}};
Output : Idempotent Matrix

Input : mat[N][N] = {{2, -2, -4},
                     {-1, 3, 4},
                     {1, -2, -3}}
Output : Idempotent Matrix.

C++

filter_none

edit
close

play_arrow

link
brightness_4
code

// Program to check given matrix 
// is idempotent matrix or not.
#include<bits/stdc++.h>
#define N 3
using namespace std;
  
// Function for matrix multiplication.
void multiply(int mat[][N], int res[][N])
{
    for (int i = 0; i < N; i++)
    {
        for (int j = 0; j < N; j++)
        {
            res[i][j] = 0;
            for (int k = 0; k < N; k++)
                res[i][j] += mat[i][k] * mat[k][j];
        }
    }
}
  
// Function to check idempotent
// property of matrix.
bool checkIdempotent(int mat[][N])
{   
    // Calculate multiplication of matrix
    // with itself and store it into res.
    int res[N][N];
    multiply(mat, res);
  
    for (int i = 0; i < N; i++)    
        for (int j = 0; j < N; j++)        
            if (mat[i][j] != res[i][j])
                return false;
    return true;
}
  
// Driver function.
int main()
{
    int mat[N][N] = {{2, -2, -4},
                    {-1, 3, 4},
                    {1, -2, -3}};
      
    // checkIdempotent function call.
    if (checkIdempotent(mat))
        cout << "Idempotent Matrix";
    else
        cout << "Not Idempotent Matrix.";
    return 0;
}

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

// Java program to check given matrix 
// is idempotent matrix or not.
import java.io.*;
  
class GFG 
{
    static int N = 3;
      
    // Function for matrix multiplication.
    static void multiply(int mat[][], int res[][])
    {
        for (int i = 0; i < N; i++)
        {
            for (int j = 0; j < N; j++)
            {
                res[i][j] = 0;
                for (int k = 0; k < N; k++)
                    res[i][j] += mat[i][k] * mat[k][j];
            }
        }
    }
      
    // Function to check idempotent
    // property of matrix.
    static boolean checkIdempotent(int mat[][])
    
        // Calculate multiplication of matrix
        // with itself and store it into res.
        int res[][] = new int[N][N];
        multiply(mat, res);
      
        for (int i = 0; i < N; i++)
        
            for (int j = 0; j < N; j++)
            {
                if (mat[i][j] != res[i][j])
                    return false;
            }
        }
        return true;
    }
  
    // Driver code.
    public static void main (String[] args) 
    {
        int mat[][] = {{2, -2, -4},
                       {-1, 3, 4},
                       {1, -2, -3}};
      
        // checkIdempotent function call.
        if (checkIdempotent(mat))
            System.out.println( "Idempotent Matrix");
        else
            System.out.println("Not Idempotent Matrix.");
          
    }
}
  
// This code is contributed by vt_m.

chevron_right


Python 3

filter_none

edit
close

play_arrow

link
brightness_4
code

# Python Program to check given matrix 
# is idempotent matrix or not.
import math
  
# Function for matrix multiplication.
def multiply(mat, res):
  
    N= len(mat)
    for i in range(0,N):
      
        for j in range(0,N):
          
            res[i][j] = 0
            for k in range(0,N):
                res[i][j] += mat[i][k] * mat[k][j]
  
# Function to check idempotent
# property of matrix.
def checkIdempotent(mat):
  
    N= len(mat)
    # Calculate multiplication of matrix
    # with itself and store it into res.
    res =[[0]*N for i in range(0,N)]
    multiply(mat, res)
  
    for i in range(0,N):
        for j in range(0,N):     
            if (mat[i][j] != res[i][j]):
                return False
    return True
  
# driver Function
mat = [ [2, -2, -4],
        [-1, 3, 4],
        [1, -2, -3] ]
      
# checkIdempotent function call.
if (checkIdempotent(mat)):
    print("Idempotent Matrix")
else:
    print("Not Idempotent Matrix.")
  
# This code is contributed by Gitanjali.

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// C# program to check given matrix 
// is idempotent matrix or not.
using System;
  
class GFG 
{
    static int N = 3;
      
    // Function for matrix multiplication.
    static void multiply(int [,]mat, int [,]res)
    {
        for (int i = 0; i < N; i++)
        {
            for (int j = 0; j < N; j++)
            {
                res[i,j] = 0;
                for (int k = 0; k < N; k++)
                    res[i,j] += mat[i,k] * mat[k,j];
            }
        }
    }
      
    // Function to check idempotent
    // property of matrix.
    static bool checkIdempotent(int [,]mat)
    
        // Calculate multiplication of matrix
        // with itself and store it into res.
        int [,]res = new int[N,N];
        multiply(mat, res);
      
        for (int i = 0; i < N; i++)
        
            for (int j = 0; j < N; j++)
            {
                if (mat[i,j] != res[i,j])
                    return false;
            }
        }
        return true;
    }
  
    // Driver code
    public static void Main () 
    {
        int [,]mat = {{2, -2, 4},
                    {-1, 3, 4},
                    {1, -2, -3}};
      
        // checkIdempotent function call.
        if (checkIdempotent(mat))
            Console.WriteLine( "Idempotent Matrix");
        else
            Console.WriteLine("Not Idempotent Matrix.");
          
    }
}
  
// This code is contributed by vt_m.

chevron_right



Output

Idempotent Matrix


My Personal Notes arrow_drop_up

Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.




Article Tags :
Practice Tags :


Be the First to upvote.


Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.