# Java Program to Check Whether a Given Matrix is an Identity Matrix

In the previous article, we have discussed Java Program to Check Whether a Given Matrix is a Sparse Matrix

In this article we are going to see how we can write a program to check if a matrix is an identity matrix in JAVA language.

## Java Program to Check Whether Two Matrices are Equal or Not

A 3*3 Matrix is having 3 rows and 3 columns where this 3*3 represents the dimension of the matrix. Means there are 3*3 i.e. total 9 elements in a 3*3 Matrix.

Let’s understand it in more simpler way.

                   | A00   A01   A02 |
Matrix A =  | A10   A11   A12 |
| A20   A21   A22 | 3*3
• Matrix A represents a 3*3 matrix.
• A‘ represents the matrix element
• Aij‘ represents the matrix element at it’s matrix position/index.
• i‘ represents the row index
• j‘ represents the column index
• Means A00=Aij  where i=0 and j=0A01=aij where i=0 and j=1 and like this.
• Here we have started row value from 0 and column value from 0.

Identity matrix is a matrix which has ones(1s) as its principal diagonal elements and rest elements are zeroes(0s).

                                1  0  0
Identity Matrix =     0  1  0
0  0  1

Let’s see different ways to check whether a given matrix is an Identity matrix or not.

### Method-1: Java Program to Check Whether a Given Matrix is an Identity Matrix By Static Initialization of Array Elements

Approach:

• Initialize and declare an array with elements.
• Using two for loops to iterate the rows and columns. Then check whether all primary diagonal elements are 1 and non-primary diagonal elements are 0.
• If the conditions are true , then it is a identity matrix, else not .

Program:

public class matrix

{
public static void main(String args[])
{
// Initializing the 3X3 matrix i.e. 2D array
int arr[][] = {{1,0,0},{0,1,0},{0,0,1}};
int row, col;
boolean flag = true;

System.out.print("The matrix elements are:");
printMatrix(arr);

// Loops to find transpose of the matrix
for(row=0;row<3;row++)
for(col=0;col<3;col++)
{
// Checks wether the primary diagonal elements are 1 or not
if(row==col)
{
if(arr[row][col]!=1)
{
flag = false;
break;
}
}
// Checks wether the non-primary diagonal elements are 0 or not
else
{
if(arr[row][col]!=0)
{
flag = false;
break;
}
}

}

if(flag)
System.out.println("\nIt is an identity matrix");
else
System.out.println("\nIt is not an identity matrix");
}

// Function to print the matrix
static void printMatrix(int arr[][])
{
int row, col;
// Loop to print the elements
for(row=0;row<3;row++)
{
// Used for formatting
System.out.print("\n");
for(col=0;col<3;col++)
{
System.out.print(arr[row][col]+" ");
}
}
System.out.print("\n");
}
}

Output:

The matrix elements are:
1 0 0
0 1 0
0 0 1

It is an identity matrix

### Method-2: Java Program to Check Whether a Given Matrix is an Identity Matrix By Dynamic Initialization of Array Elements

Approach:

• Initialize two arrays of size 3×3.
• Ask the user for input off array elements and store them in the arrays using two for loops.
• Using two for loops to iterate the rows and columns. Then check whether all primary diagonal elements are 1 and non-primary diagonal elements are 0.
• If the conditions are true , then it is a identity matrix, else not .

Program:

import java.util.Scanner;
public class matrix{
public static void main(String args[])
{
//Scanner class to take input
Scanner scan = new Scanner(System.in);

// Initializing the 3X3 matrix i.e. 2D array
int arr[][] = new int;
int row, col;
boolean flag = true;

// Taking matrix input
System.out.println("\nEnter the matrix elements : ");
for(row=0;row<3;row++)
for(col=0;col<3;col++)
arr[row][col] = scan.nextInt();

System.out.print("The matrix elements are : ");
printMatrix(arr);

// Loops to find transpose of the matrix
for(row=0;row<3;row++)
for(col=0;col<3;col++)
{
// Checks wether the primary diagonal elements are 1 or not
if(row==col)
{
if(arr[row][col]!=1)
{
flag = false;
break;
}
}
// Checks wether the non-primary diagonal elements are 0 or not
else
{
if(arr[row][col]!=0)
{
flag = false;
break;
}
}

}

if(flag)
System.out.println("\nIt is an identity matrix");
else
System.out.println("\nIt is not an identity matrix");
}

// Function to print the matrix
static void printMatrix(int arr[][])
{
int row, col;
// Loop to print the elements
for(row=0;row<3;row++)
{
// Used for formatting
System.out.print("\n");
for(col=0;col<3;col++)
{
System.out.print(arr[row][col]+" ");
}
}
System.out.print("\n");
}
}

Output:

Enter the matrix elements : 1  0 0 0 1 0 0 0 1
The matrix elements are :
1 0 0
0 1 0
0 0 1

It is an identity matrix

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