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.

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.

Implementation:

C++

// 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;
}

Java

// 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.

Python 3

# 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.

C#

// 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.

Javascript

<script>

// Javascript program to check given matrix
// is idempotent matrix or not.
var N = 3;

// Function for matrix multiplication.
function multiply(mat, res)
{
    for (var i = 0; i < N; i++)
    {
        for (var j = 0; j < N; j++)
        {
            res[i][j] = 0;
            for (var k = 0; k < N; k++)
                res[i][j] += mat[i][k] * mat[k][j];
        }
    }
    return res;
}

// Function to check idempotent
// property of matrix.
function checkIdempotent(mat)
{

    // Calculate multiplication of matrix
    // with itself and store it into res.
    var res = Array.from(Array(N), ()=>Array(N).fill(0));
    res = multiply(mat, res);

    for (var i = 0; i < N; i++)
    {
        for (var j = 0; j < N; j++)
        {
            if (mat[i][j] != res[i][j])
                return false;
        }
    }
    return true;
}

// Driver code
var mat = [[2, -2, -4],
            [-1, 3, 4],
            [1, -2, -3]];

// checkIdempotent function call.
if (checkIdempotent(mat))
    document.write( "Idempotent Matrix");
else
    document.write("Not Idempotent Matrix.");

// This code is contributed by noob2000.
</script>

Output

Idempotent Matrix

Time Complexity: O(n³)
Auxiliary Space: O(n²), since n² extra space has been taken.