# Check Involuntary Matrix

“** Check Involuntary Matrix**” is a problem of matrix where we need to check whether given matrix is an involuntary matrix or not.

There are basically three different types of matrix:

: An identity matrix is a square matrix of size N*N which have all the diagonal element as 1 and others as 0.*Identity Matrix*: An Idempotent matrix is a matrix which is when multiplied by itself produces the same matrix.*Idempotent Matrix*: An involutory matrix is a matrix which when multiplied by itself gives identity matrix.*Involuntary Matrix*

Here, we are given a square matrix of size N*N. Our task is to check whether the given matrix is involuntary matrix or not.

**Example:**

N=3 1 0 0 0 -1 0 0 0 -1INPUT:Involutory Matrix!!OUTPUT:

The solution of the above problem is to multiply the given matrix by itself and store the result in resultant matrix. If the resultant matrix identity matrix, then given matrix is said to be involutory matrix. Else, it is not an involutory matrix.

**C++ Program to check whether given matrix is involutory matrix or not is as follows:**

#include<bits/stdc++.h> using namespace std; int main() { // Scan Dimension of the matrix int n; cout<<"Enter the dimesion of square matrix:\n"; cin>>n; // Scan Elements of the matrix int matrix[n][n]; cout<<"Enter the elements of square matrix:\n"; for(int i = 0 ; i < n ; i++) for(int j = 0 ; j < n ; j++) cin>>matrix[i][j]; // Initializing resultant matrix with 0 int resultant[n][n]; for(int i = 0 ; i < n ; i++) for(int j = 0 ; j < n ; j++) resultant[i][j] = 0; //Multiply the matrix with itself and storing // the result in resultant matrix for (int i = 0 ; i < n ; i++) { for (int j = 0 ; j < n ; j++) { for (int k = 0 ; k < n ; k++) { resultant[i][j] += matrix[i][k] * matrix[k][j]; } } } //Check whether the resultant matrix is // involuntary matrix or not bool result = true; for (int i = 0 ; i < n ; i++) { for (int j = 0 ; j < n ; j++) { if(i==j && resultant[i][j]!=1) { result = false; break; } else if(i!=j && resultant[i][j]!=0) { result = false; break; } } if(!result) break; } if(result) cout<<"Involutory Matrix!!"; else cout<<"Not Involutory Matrix"; }

Enter the dimesion of square matrix: 3 Enter the elements of square matrix: 1 0 0 0 -1 0 0 0 -1 Involutory Matrix!!OUTPUT:

**Related Posts:**

**Program to print matrix in zig-zag order.****Program to print matrix in spiral order.****Program to sort a matrix.****Program to Add two Matrix.****Program to Transpose a Matrix.****Program to Multiply Two Matrix.****Program to check Identity Matrix.****Program to check Idempotent Matrix.****Program to count total number of words in a string.****Program to find smallest and largest word of the String.****Program to find Most Frequent Character of the String.****Program to Remove all the blank spaces from the String.****Program to check if String is isogram or not.****Program to Reverse Each word of the String.****Program to Print All the Substring of the Given String.****Program to find longest palindromic Substring.****Program to check Anagram Strings.****Program to check whether two Strings are Rotation of each other or not.****Program to check Palindromic Anagram.****Program to print all the Palindromic Substring of the String.**