# 检查幂等矩阵的程序 > 原文： [https://www.geeksforgeeks.org/program-check-idempotent-matrix/](https://www.geeksforgeeks.org/program-check-idempotent-matrix/) 给定一个 N * N 矩阵，任务是检查矩阵是否为等幂矩阵。 [**等幂矩阵：**](https://en.wikipedia.org/wiki/Idempotent_matrix) 如果矩阵与自身相乘返回相同的矩阵，则称该矩阵为等幂矩阵。 当且仅当 **M * M = M** 时，矩阵 M 才是等幂矩阵。 在幂等矩阵中，M 是平方矩阵。  例子： ``` 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++ ```cpp // 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 // 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# ```cs // 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. ``` Output ``` Idempotent Matrix ``` * * * * * *