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Program for Identity Matrix

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Introduction to Identity Matrix :

 The dictionary definition of an Identity Matrix is a square matrix in which all the elements of the principal or main diagonal are 1’s and all other elements are zeros. In the below image, every matrix is an Identity Matrix. 
 


In linear algebra, this is sometimes called as a Unit Matrix, of a square matrix (size = n x n) with ones on the main diagonal and zeros elsewhere. The identity matrix is denoted by “ I “. Sometimes U or E is also used to denote an Identity Matrix. 

A property of the identity matrix is that it leaves a matrix unchanged if it is multiplied by an Identity Matrix.

Examples:  

Input  : 2
Output : 1 0
         0 1

Input :  4
Output : 1 0 0 0
         0 1 0 0
         0 0 1 0
         0 0 0 1
The explanation is simple. We need to make all
the elements of principal or main diagonal as 
1 and everything else as 0.

Program to print Identity Matrix: The logic is simple. You need to print 1 in those positions where row is equal to the column of a matrix and make all other positions as 0. 

Implementation

C++


                    

C


                    

Java


                    

Python3

# Python code to print identity matrix
  
# Function to print identity matrix
def Identity(size):
    for row in range(0, size):
        for col in range(0, size):
  
            # Here end is used to stay in same line
            if (row == col):
                print("1 ", end=" ")
            else:
                print("0 ", end=" ")
        print()
  
# Driver Code        
size = 5
Identity(size)

                    

C#


                    

PHP

<?php
// PHP program to print 
// Identity Matrix
  
function Identity($num)
{
    $row; $col;
      
    for ($row = 0; $row < $num; $row++)
    {
        for ($col = 0; $col < $num; $col++)
        {
              
            // Checking if row is 
            // equal to column 
            if ($row == $col)
            echo 1," ";
            else
            echo 0," ";
        
        echo"\n";
    }
    return 0;
}
  
    // Driver Code
    $size = 5;
    identity($size);
  
// This code is contributed by anuj_67.
?>

                    

Javascript


                    

Output
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
0 0 0 0 1 

Time Complexity: O(row x col)
Auxiliary Space: O(1), as no extra space is used
 
Program to check if a given square matrix is Identity Matrix : 

C++

// CPP program to check if a given matrix is identity
#include<iostream>
using namespace std;
  
const int MAX = 100;
  
bool isIdentity(int mat[][MAX], int N)
    for (int row = 0; row < N; row++)
    {
        for (int col = 0; col < N; col++)
        {
            if (row == col && mat[row][col] != 1)
                return false;
            else if (row != col && mat[row][col] != 0)
                return false;
        
    }
    return true;
}
  
// Driver Code
int main()
{
    int N = 4;
    int mat[][MAX] = {{1, 0, 0, 0}, 
                    {0, 1, 0, 0},
                    {0, 0, 1, 0},
                    {0, 0, 0, 1}}; 
    if (isIdentity(mat, N))
       cout << "Yes ";
    else
       cout << "No ";
    return 0;
}

                    

C

// C program to check identity matrix
#include <stdio.h>
  
// Function to check identity matrix
int isidentity(int a[][100], int N)
{
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < N; j++) {
            if (i == j && a[i][j] != 1)
                return 0;
            else if (i != j && a[i][j] != 0)
                return 0;
        }
    }
    return 1;
}
int main()
{
  
    // code
    int N = 4;
    int a[][100] = { { 1, 0, 0, 0 },
                     { 0, 1, 0, 0 },
                     { 0, 0, 1, 0 },
                     { 0, 0, 0, 1 } };
    if (isidentity(a, N))
        printf("Yes");
    else
        printf("No");
    return 0;
}
  
// This code is contributed by aayushi2402

                    

Java

// Java program to check if a given 
// matrix is identity
import java.io.*;
class GFG {
      
    int MAX = 100;
   
    static boolean isIdentity(int mat[][], int N)
    
        for (int row = 0; row < N; row++)
        {
            for (int col = 0; col < N; col++)
            {
                if (row == col && mat[row][col] != 1)
                    return false;
                else if (row != col && mat[row][col] != 0)
                    return false;
            
        }
        return true;
    }
       
    // Driver Code
    public static void main(String args[])
    {
        int N = 4;
        int mat[][] = {{1, 0, 0, 0},
                       {0, 1, 0, 0},
                       {0, 0, 1, 0},
                       {0, 0, 0, 1}}; 
          
        if (isIdentity(mat, N))
           System.out.println("Yes ");
        else
           System.out.println("No ");
    }
}
  
  
/*This code is contributed by Nikita Tiwari.*/

                    

Python3

# Python3 program to check 
# if a given matrix is identity
MAX = 100;
def isIdentity(mat, N):
    for row in range(N):
        for col in range(N):
            if (row == col and 
                mat[row][col] != 1):
                return False;
            elif (row != col and 
                  mat[row][col] != 0):
                return False;
    return True;
  
# Driver Code
N = 4;
mat = [[1, 0, 0, 0],
       [0, 1, 0, 0],
       [0, 0, 1, 0],
       [0, 0, 0, 1]]; 
if (isIdentity(mat, N)):
    print("Yes ");
else:
    print("No ");
  
# This code is contributed
# by mits

                    

C#

// C# program to check if a given 
// matrix is identity
using System;
  
class GFG {
      
    //int MAX = 100;
  
    static bool isIdentity(int[,] mat, int N)
    
        for (int row = 0; row < N; row++)
        {
            for (int col = 0; col < N; col++)
            {
                if (row == col && mat[row,col] != 1)
                    return false;
                else if (row != col && mat[row,col] != 0)
                    return false;
            
        }
        return true;
    }
      
    // Driver Code
    public static void Main()
    {
        int N = 4;
        int [,]mat = {{1, 0, 0, 0},
                      {0, 1, 0, 0},
                      {0, 0, 1, 0},
                      {0, 0, 0, 1}}; 
          
        if (isIdentity(mat, N))
        Console.WriteLine("Yes ");
        else
        Console.WriteLine("No ");
    }
}
  
  
/*This code is contributed by vt_m.*/

                    

PHP

<?php
// PHP program to check if a
// given matrix is identity
// $MAX = 100;
  
function isIdentity($mat, $N)
    for ($row = 0; $row < $N; $row++)
    {
        for ( $col = 0; $col < $N; $col++)
        {
            if ($row == $col and 
                $mat[$row][$col] != 1)
                return false;
            else if ($row != $col && 
                     $mat[$row][$col] != 0)
                return false;
        
    }
    return true;
}
  
    // Driver Code
    $N = 4;
    $mat = array(array(1, 0, 0, 0), 
                 array(0, 1, 0, 0),
                 array(0, 0, 1, 0),
                 array(0, 0, 0, 1)); 
    if (isIdentity($mat, $N))
    echo "Yes ";
    else
    echo "No ";
  
// This code is contributed by anuj_67.
?>

                    

Javascript

<script>
  
// JavaScript program to check if a given
// matrix is identity
let MAX = 100;
  
function isIdentity(mat, N)
{
    for(let row = 0; row < N; row++)
    {
        for(let col = 0; col < N; col++)
        {
            if (row == col && mat[row][col] != 1)
                return false;
            else if (row != col && mat[row][col] != 0)
                return false;
        }
    }
    return true;
}
  
// Driver Code
let N = 4;
let mat = [ [ 1, 0, 0, 0 ],
            [ 0, 1, 0, 0 ],
            [ 0, 0, 1, 0 ],
            [ 0, 0, 0, 1 ] ];
   
if (isIdentity(mat, N))
    document.write("Yes ");
else
    document.write("No ");
      
// This code is contributed by sanjoy_62
  
</script>

                    

Output
Yes 

Time Complexity: O(row x col)
Auxiliary Space: O(1), as no extra space is used

 



Last Updated : 17 Feb, 2023
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