Identity Matrix in C++

This is a C++ Program to Find if an Array is an Identity Matrix.

Problem Description

The program takes a array and checks if it is an identity matrix. An identity matrix is a square matrix with main diagonal elements as 1 and rest 0.

Problem Solution

1. The program takes the number of rows and columns of the matrix.
2. If they are not equal, it cannot be an identity matrix. The program is exited.
3. Else, the matrix is checked if only the main diagonal elements are 1 and rest are 0.
4. The result is printed.
5. Exit.

C++ Program/Source code

Here is the source code of C++ Program to Find if an Array is an Identity Matrix. The program output is shown below.

```
#include<iostream>
```
```
using namespace std;
```
```
int main ()
```
```
{
```

    int i, j, m, n, A[10][10], flag = 0;

    cout << "Enter number of rows and columns : ";

```
    cin >> m >> n;
```
```
    if (m != n)
```
```
    {
```

        cout << "Matrix is not a square matrix!";

```
        exit(0);
```
```
    }
```
```
    cout << "Enter array elements : ";
```
```
    for (i = 0; i < m; i++)
```
```
        for (j = 0; j < n; j++)    
```
```
            cin >> A[i][j];
```
```
    for (i = 0; i < m; i++)
```
```
        for (j = 0; j < n; j++)
```
```
        {
```

            if ((A[i][j] != 1) && (A[j][i] != 0))

```
            {
```
```
                flag = 1;
```
```
                break;
```
```
            }
```
```
        }
```
```
    if (flag == 0)
```

        cout << "The given array is an identity matrix.\n ";

```
    else
```

        cout << "The given array is not an identity matrix.\n ";

```
    for (i = 0; i < m; i++)
```
```
    {
```
```
        for (j = 0; j < n; j++)	
```
```
            cout << A[i][j] << " ";
```
```
        cout << "\n ";
```
```
    }
```
```
    return 0;
```
```
}
```

Program Explanation

1. The user is asked to enter the number of rows and columns.
2. If they are not equal, the array is not a square matrix, hence it cannot be an identity matrix. The program is exited.
3. Else, the elements are asked to enter and stored in ‘A’.
4. If the diagonal elements of the matrix are not 1 and non diagonal elements are not 0, the variable ‘flag’ is assigned value 1.
5. If flag is equal to 0, the entered array is an identity matrix, else it is not.
6. The result is then printed.

Runtime Test Cases

Case 1 :
Enter number of rows and columns : 2 2
Enter array elements : 1 2 3 4
The given array is not an identity matrix.
 1 2
 3 4
 
Case 2 :
Enter number of rows and columns : 3 2
Matrix is not a square matrix!
 
Case 3 :
Enter number of rows and columns : 3 3
Enter array elements : 1 0 0 0 1 0 0 0 1
The given array is an identity matrix.
 1 0 0
 0 1 0
 0 0 1

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