程序检查对合矩阵

给定一个矩阵，任务是检查矩阵是否为非强制矩阵。
非对偶矩阵：如果矩阵自身乘以返回恒等矩阵，则称该矩阵为非对偶矩阵。对合矩阵是其自身的逆矩阵。如果A * A = I，则矩阵A被称为对合矩阵。我是单位矩阵。

例子：

Input : mat[N][N] = {{1, 0, 0},
                     {0, -1, 0},
                     {0, 0, -1}}
Output : Involutory Matrix

Input : mat[N][N] = {{1, 0, 0},
                     {0, 1, 0},
                     {0, 0, 1}} 
Output : Involutory Matrix

C++

// Program to implement involutory matrix.
#include 
#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 involutory matrix.
bool InvolutoryMatrix(int mat[N][N])
{
    int res[N][N];
  
    // multiply function call.
    multiply(mat, res);
  
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < N; j++) {
            if (i == j && res[i][j] != 1)
                return false;
            if (i != j && res[i][j] != 0)
                return false;
        }
    }
    return true;
}
  
// Driver function.
int main()
{
    int mat[N][N] = { { 1, 0, 0 },
                      { 0, -1, 0 },
                      { 0, 0, -1 } };
  
    // Function call. If function return
    // true then if part will execute otherwise
    // else part will execute.
    if (InvolutoryMatrix(mat))
        cout << "Involutory Matrix";
    else
        cout << "Not Involutory Matrix";
  
    return 0;
}

Java

// Java  Program to implement 
// involutory matrix.
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 involutory matrix.
    static boolean InvolutoryMatrix(int mat[][])
    {
        int res[][] = new int[N][N];
      
        // multiply function call.
        multiply(mat, res);
      
        for (int i = 0; i < N; i++) {
            for (int j = 0; j < N; j++) {
                if (i == j && res[i][j] != 1)
                    return false;
                if (i != j && res[i][j] != 0)
                    return false;
            }
        }
        return true;
    }
      
    // Driver function.
    public static void main (String[] args) 
    {
          
        int mat[][] = { { 1, 0, 0 },
                        { 0, -1, 0 },
                        { 0, 0, -1 } };
      
        // Function call. If function return
        // true then if part will execute 
        // otherwise else part will execute.
        if (InvolutoryMatrix(mat))
            System.out.println ( "Involutory Matrix");
        else
            System.out.println ( "Not Involutory Matrix");
      
              
    }
}
  
// This code is contributed by vt_m

Python3

# Program to implement involutory matrix.
N = 3;
  
# Function for matrix multiplication.
def multiply(mat, res):
  
    for i in range(N): 
        for j in range(N):
            res[i][j] = 0;
            for k in range(N):
                res[i][j] += mat[i][k] * mat[k][j];
    return res;
  
# Function to check involutory matrix.
def InvolutoryMatrix(mat):
  
    res=[[0 for i in range(N)] 
            for j in range(N)];
  
    # multiply function call.
    res = multiply(mat, res);
  
    for i in range(N): 
        for j in range(N):
            if (i == j and res[i][j] != 1):
                return False;
            if (i != j and res[i][j] != 0):
                return False;
    return True;
  
# Driver Code
mat = [[1, 0, 0], [0, -1, 0], [0, 0, -1]];
  
# Function call. If function 
# return true then if part 
# will execute otherwise
# else part will execute.
if (InvolutoryMatrix(mat)):
    print("Involutory Matrix");
else:
    print("Not Involutory Matrix");
  
# This code is contributed by mits

C#

// C# Program to implement 
// involutory matrix.
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 involutory matrix.
    static bool InvolutoryMatrix(int [,]mat)
    {
        int [,]res = new int[N,N];
      
        // multiply function call.
        multiply(mat, res);
      
        for (int i = 0; i < N; i++) {
            for (int j = 0; j < N; j++) {
                if (i == j && res[i,j] != 1)
                    return false;
                if (i != j && res[i,j] != 0)
                    return false;
            }
        }
        return true;
    }
      
    // Driver function.
    public static void Main () 
    {
          
        int [,]mat = { { 1, 0, 0 },
                        { 0, -1, 0 },
                        { 0, 0, -1 } };
      
        // Function call. If function return
        // true then if part will execute 
        // otherwise else part will execute.
        if (InvolutoryMatrix(mat))
            Console.WriteLine( "Involutory Matrix");
        else
            Console.WriteLine( "Not Involutory Matrix");
      
              
    }
}
  
// This code is contributed by vt_m

输出 ：

Involutory Matrix