Program to check idempotent matrix in C++

Given a matrix M[r][c], ‘r’ denotes number of rows and ‘c’ denotes number of columns such that r = c forming a square matrix. We have to check whether the given square matrix is an Idempotent matrix or not.

Idempotent Matrix

A matrix ‘M’ is called Idempotent matrix if and only the matrix ‘M’ multiplied by itself returns the same matrix ‘M’ i.e. M * M = M.

Like in the given example below −

We can say that the above matrix is multiplied by itself and returns the same matrix; hence the matrix is Idempotent matrix.

Example

Input: m[3][3] = { {2, -2, -4},
   {-1, 3, 4},
   {1, -2, -3}}
Output: Idempotent
Input: m[3][3] == { {3, 0, 0},
   {0, 2, 0},
   {0, 0, 3} }
Output: Not Idempotent

Algorithm

Start
Step 1 -> define macro as #define size 3
Step 2 -> declare function for matrix multiplication
   void multiply(int arr[][size], int res[][size])
      Loop For int i = 0 and i < size and i++
         Loop For int j = 0 and j < size and j++
            Set res[i][j] = 0
            Loop for int k = 0 and k < size and k++
               Set res[i][j] += arr[i][k] * arr[k][j]
            End
      End
   End
Step 3 -> declare function to check idempotent or not
   bool check(int arr[][size])
   declare int res[size][size]
   call multiply(arr, res)
      Loop For int i = 0 and i < size and i++
      Loop For int j = 0 and j < size and j++
         IF (arr[i][j] != res[i][j])
            return false
         End
      End
   End
   return true
step 4 -> In main()
   declare int arr[size][size] = {{1, -1, -1},
      {-1, 1, 1},
      {1, -1, -1}}
   IF (check(arr))
      Print its an idempotent matrix
   Else
      Print its not an idempotent matrix
Stop

Example

#include<bits/stdc++.h>
#define size 3
using namespace std;
//matrix multiplication.
void multiply(int arr[][size], int res[][size]){
   for (int i = 0; i < size; i++){
      for (int j = 0; j < size; j++){
         res[i][j] = 0;
         for (int k = 0; k < size; k++)
            res[i][j] += arr[i][k] * arr[k][j];
      }
   }
}
//check idempotent or not
bool check(int arr[][size]){
   int res[size][size];
   multiply(arr, res);
   for (int i = 0; i < size; i++)
   for (int j = 0; j < size; j++)
      if (arr[i][j] != res[i][j])
         return false;
   return true;
}
int main(){
   int arr[size][size] = {{1, -1, -1},
      {-1, 1, 1},
      {1, -1, -1}};
   if (check(arr))
      cout << "its an idempotent matrix";
   else
      cout << "its not an idempotent matrix";
   return 0;
}