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C++ Program to check idempotent matrix

  • Last Updated : 18 Jan, 2022

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++




// 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;
}

Output:

Idempotent Matrix

Please refer complete article on Program to check idempotent matrix for more details!


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