Program to check Identity Matrix

Given a square matrix mat[][] of order n*n, the task is to check if it is an Identity Matrix.

Identity Matrix: A square matrix is said to be an identity matrix if the elements of main diagonal are one and all other elements are zero. The identity Matrix is also known as the Unit Matrix.

Examples: 

Input: mat[][] = [[1, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]]

Output: True
Explanation: Main Diagonal = [1, 1, 1, 1], elements of main diagonal are one and all other elements are zero.

Input: mat[][] = [[6, 10, 12, 0],
[0, 5, 0, 0],
[0, 0, 9, 0],
[0, 0, 0, 1]]

Output: False
Explanation: Main Diagonal = [6, 5, 9, 1], elements of main diagonal are not one.

Approach:

The row and column indexes of Primary or Major diagonal are same i.e. lets say mat[][] is matrix then mat[i][i] will be a Major Diagonal element. The idea is to traverse the matrix and check if main diagonal's elements are one and all other elements are zero.

// C++ Program to check matrix is Identity matrix or not.
#include <bits/stdc++.h>
using namespace std;

// Function to check matrix
// is Identity matrix or not.
bool isIdentityMatrix(vector<vector<int>> &mat) {
    int n = mat.size();
    for (int i = 0; i < n; i++) {

        // condition to check main diagonal
        // elements are equal to 1 or not.
        if(mat[i][i] != 1)
            return false;

        for (int j = 0; j < n; j++) {

            // condition to check other elements 
            // except main diagonal are zero or not.
            if ((i != j) && (mat[i][j] != 0))
                return false;
            
        }
    }
    return true;
}

int main() {
    vector<vector<int>> mat = { { 1, 0, 0, 0 },
                      { 0, 1, 0, 0 },
                      { 0, 0, 1, 0 },
                      { 0, 0, 0, 1 } };

    if (isIdentityMatrix(mat))
        cout << "True" << endl;
    else
        cout << "False" << endl;
    return 0;
}

// Java Program to check matrix is Identity matrix or not.
import java.util.*;

class GfG {

    // Function to check matrix
    // is Identity matrix or not.
    static boolean isIdentityMatrix(int[][] mat) {
      
        int n = mat.length;
        for (int i = 0; i < n; i++) {

            // condition to check main diagonal
            // elements are equal to 1 or not.
            if(mat[i][i] != 1)
                return false;

            for (int j = 0; j < n; j++) {

                // condition to check other elements 
                // except main diagonal are zero or not.
                if ((i != j) && (mat[i][j] != 0))
                    return false;
            }
        }

        return true;
    }

    public static void main(String[] args) {
        int[][] mat = {
            { 1, 0, 0, 0 },
            { 0, 1, 0, 0 },
            { 0, 0, 1, 0 },
            { 0, 0, 0, 1 }
        };

        if (isIdentityMatrix(mat))
            System.out.println("True");
        else
            System.out.println("False");
    }
}

# Python Program to check if matrix
# is Identity matrix or not.

def isIdentityMatrix(mat):
    n = len(mat)
    for i in range(0, n):

        # condition to check main diagonal
        # elements are equal to 1 or not.
        if (mat[i][i] != 1) :
            return False
        
        for j in range(0, n) :
            
            # condition to check other elements 
            # except main diagonal are zero or not.
            if ((i != j) and (mat[i][j] != 0)) :
                return False

    return True

mat = [[ 1, 0, 0, 0 ],
       [ 0, 1, 0, 0 ],
       [ 0, 0, 1, 0 ],
       [ 0, 0, 0, 1 ]]

if (isIdentityMatrix(mat)) :
    print("True")
else :
    print("False")

// C# Program to check matrix is
// Identity matrix or not.
using System;

class GfG {
  
    // Function to check matrix
 	// is Identity matrix or not.
    static bool isIdentityMatrix(int [,]mat) {
      
      	int n = mat.GetLength(0);
        for (int i = 0; i < n; i++) {

            // condition to check main diagonal
            // elements are equal to 1 or not.
            if(mat[i,i] != 1)
                return false;

            for (int j = 0; j < n; j++) {
    
                // condition to check other elements 
                // except main diagonal are zero or not.
                if ((i != j) && (mat[i,j] != 0))
                    return false;
            }
        }

        return true;
    }
    
    static void Main() {
        int [,]mat = { { 1, 0, 0, 0 },
                        { 0, 1, 0, 0 },
                        { 0, 0, 1, 0 },
                        { 0, 0, 0, 1 } };
    
        if (isIdentityMatrix(mat))
            Console.WriteLine("True");
        else
            Console.WriteLine("False");
    }
}

// JavaScript program to check matrix is
// Identity matrix or not.

// Function to check matrix
// is Identity matrix or not.
function isIdentityMatrix(mat) {

    let n = mat.length;
    for (let i = 0; i < n; i++){

        // condition to check main diagonal
        // elements are equal to 1 or not.
        if(mat[i][i] != 1)
            return false;
        for (let j = 0; j < n; j++){

            // condition to check other elements 
            // except main diagonal are zero or not.
            if ((i != j) &&
                (mat[i][j] != 0))
                return false;
        }
    }

    return true;
}

//driver code
let mat = [[1, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]];

if (isIdentityMatrix(mat))
    console.log("True");
else
    console.log("False");

True

Time Complexity: O(n²)
Auxiliary Space: O(1), as no extra space is used