# Check Identity Matrix

Check Identity Matrix” is a problem of matrix, where we need to check whether given matrix is an identity matrix or not.

There are basically three different types of matrix:

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

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

Example:

```INPUT:
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
OUTPUT:
TRUE
```

#### C++ Program to check Identity Matrix is as follows:

```/* Program to check Identity Matrix */
#include<bits/stdc++.h>
using namespace std;
int main()
{
int N;
// Scan Dimensions of the matrix
cout<<"Enter the dimension of the matrix:\n";
cin>>N;

int matrix[N][N];

// Scan Matrix Elements
cout<<"Enter the elements of the matrix:\n";
for(int i = 0 ; i < N ; i++)
for(int j = 0 ; j < N ; j++)
cin>>matrix[i][j];

bool result = true;

// Check Identity matrix
for(int i = 0 ; i < N ; i++)
{
for(int j = 0 ; j < N ; j++)
{
if(i==j && matrix[i][j]!=1)
{
result = false;
break;
}
else if(i!=j && matrix[i][j]!=0)
{
result = false;
break;
}
}
if(!result)
break;
}

// Print the result
if(result)
cout<<"The Matrix is Identity Matrix";
else
cout<<"The Matrix is not Identity Matrix";
}

```
```OUTPUT:
Enter the dimension of the matrix: 3
Enter the elements of the matrix:
1 0 0
0 1 0
0 0 1
The Matrix is Identity Matrix```

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