# Java Program to Check Whether a Matrix is Symmetric or Not

In this article we are going to see how we can check if a matrix is symmetric or not in JAVA language.

## Java Program to Check Whether a Matrix is Symmetric 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=0,  A01=aij where i=0 and j=1 and like this.
• Here we have started row value from 0 and column value from 0.

A symmetric matrix is a matrix which is the same as its transpose.

For example-

1 2 3
2 3 1
3 1 3

Let’s see different ways to print boundary elements of a matrix.

### Method-1: Java Program to Check Whether a Matrix is Symmetric or Not By Static Initialization of Array Elements

Approach:

• Initialize and declare two array of size 3×3 with elements.
• Find out the transpose of the matrix and compare all the elements with the main matrix.
• If all elements are same then it is said to be a symmetric matrix else not.

Program:

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

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

temp = trans(arr);
boolean flag = true;

// Checks whether the matrix elements are in the same position as the transpose
for(row=0;row<3;row++)
for(col=0;col<3;col++)
if(arr[row][col] != temp[row][col])
{
flag = false;
break;
}

if(flag)
System.out.println("\nIt is a symmetric matrix");
else
System.out.println("\nIt is not a symmetric matrix");

}

// Method 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");
}

// Method to find the transpose
static int[][] trans(int[][] mat)
{
int row, col, trans[][] = new int;
for(row=0;row<3;row++)
for(col=0;col<3;col++)
trans[row][col] = mat[col][row];
System.out.print("The transpose of matrix is :");
printMatrix(trans);
return trans;
}

}


Output:

The matrix is :
1 2 3
2 3 1
3 1 3
The transpose of matrix is :
1 2 3
2 3 1
3 1 3

It is a symmetric matrix

### Method-2: Java Program to Check Whether a Matrix is Symmetric or Not By Dynamic Initialization of Array Elements

Approach:

• Declare two array of size 3×3 with elements.
• Take the input of array elements for main matrix.
• Find out the transpose of the matrix and compare all the elements with the main matrix.
• If all elements are same then it is said to be a symmetric 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, temp[][] = new int;
int row, col;

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

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

temp = trans(arr);
boolean flag = true;

// Checks whether the matrix elements are in the same position as the transpose
for(row=0;row<3;row++)
for(col=0;col<3;col++)
if(arr[row][col] != temp[col][row])
{
flag = false;
break;
}

if(flag)
System.out.println("\nIt is a symmetric matrix");
else
System.out.println("\nIt is not a symmetric matrix");

}

// Method 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");
}

// Method to find the transpose
static int[][] trans(int[][] mat)
{
int row, col, trans[][] = new int;
for(row=0;row<3;row++)
for(col=0;col<3;col++)
trans[row][col] = mat[col][row];

System.out.print("The transpose of matrix is :");
printMatrix(trans);
return trans;
}

}


Output:

Enter matrix elements :
The matrix is :
1 2 3
2 3 1
3 1 3
The transpose of matrix is :
1 2 3
2 3 1
3 1 3

It is a symmetric matrix

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