# Check Involuntary Matrix

“** Check Involuntary Matrix**” is a basic 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 to check involuntary matrix 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 Involuntary Matrix is as follows:**

/* Program to Check Involuntary Matrix */ #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:

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