Program to check Involutory 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 Involutory matrix or not.

Involutory Matrix

A matrix is called Involutory matrix if and only if, when a matrix gets multiplied with itself and its result is an identity matrix. A matrix I is Identity matrix if and only if its main diagonal is one and other elements than the main diagonal are zero. So, we can say a matrix is Involutory matrix if and only if M*M=I, where M is some matrix and I is an Identity Matrix.

Like in the given Example below −

Here when we multiplied the matrix with itself the result is the identity matrix; hence the given matrix is Involutory Matrix.

Example

Input: { {1, 0, 0},
   {0, -1, 0},
   {0, 0, -1}}
Output: yes
Input: { {3, 0, 0},
   {0, 2, 0},
   {0, 0, 3} }
Output: no

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 involutory matrix or not
   bool check(int arr[size][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 (i == j && res[i][j] != 1)
            return false
         End
         If (i != j && res[i][j] != 0)
            return false
         End
      End
   End
   Return true
Step 4 -> In main()
   Declare int arr[size][size] = { { 1, 0, 0 },
      { 0, -1, 0 },
      { 0, 0, -1 } }
   If (check(arr))
      Print its an involutory matrix
   Else
      Print its not an involutory 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 involutory matrix or not.
bool check(int arr[size][size]){
   int res[size][size];
   multiply(arr, res);
   for (int i = 0; i < size; i++){
      for (int j = 0; j < size; j++){
         if (i == j && res[i][j] != 1)
            return false;
         if (i != j && res[i][j] != 0)
            return false;
      }
   }
   return true;
}
int main(){
   int arr[size][size] = { { 1, 0, 0 },
      { 0, -1, 0 },
      { 0, 0, -1 } };
   if (check(arr))
      cout << "its an involutory matrix";
   else
      cout << "its not an involutory matrix";
   return 0;
}