Program to check if a matrix is symmetric

A square matrix is said to be symmetric matrix if the transpose of the matrix is same as the given matrix. Symmetric matrix can be obtain by changing row to column and column to row.

Examples: 

Input : 1 2 3
        2 1 4
        3 4 3
Output : Yes

Input : 3 5 8
        3 4 7
        8 5 3
Output : No

A Simple solution is to do following. 

1. Create transpose of given matrix. 
2. Check if transpose and given matrices are same or not,  

Implementation:

C++

// Simple c++ code for check a matrix is
// symmetric or not.
#include <iostream>
using namespace std;

const int MAX = 100;

// Fills transpose of mat[N][N] in tr[N][N]
void transpose(int mat[][MAX], int tr[][MAX], int N)
{
    for (int i = 0; i < N; i++)
        for (int j = 0; j < N; j++)
            tr[i][j] = mat[j][i];
}

// Returns true if mat[N][N] is symmetric, else false
bool isSymmetric(int mat[][MAX], int N)
{
    int tr[N][MAX];
    transpose(mat, tr, N);
    for (int i = 0; i < N; i++)
        for (int j = 0; j < N; j++)
            if (mat[i][j] != tr[i][j])
                return false;
    return true;
}

// Driver code
int main()
{
    int mat[][MAX] = { { 1, 3, 5 },
                       { 3, 2, 4 },
                       { 5, 4, 1 } };

    if (isSymmetric(mat, 3))
        cout << "Yes";
    else
        cout << "No";
    return 0;
}

Java

// Simple java code for check a matrix is
// symmetric or not.

import java.io.*;

class GFG {



 static int  MAX = 100;

// Fills transpose of mat[N][N] in tr[N][N]
 static void transpose(int mat[][], int tr[][], int N)
{
    for (int i = 0; i < N; i++)
        for (int j = 0; j < N; j++)
            tr[i][j] = mat[j][i];
}

// Returns true if mat[N][N] is symmetric, else false
 static boolean isSymmetric(int mat[][], int N)
{
    int tr[][] = new int[N][MAX];
    transpose(mat, tr, N);
    for (int i = 0; i < N; i++)
        for (int j = 0; j < N; j++)
            if (mat[i][j] != tr[i][j])
                return false;
    return true;
}

// Driver code
    public static void main (String[] args)
 {

        int mat[][] = { { 1, 3, 5 },
                    { 3, 2, 4 },
                    { 5, 4, 1 } };

    if (isSymmetric(mat, 3))
        System.out.println( "Yes");
    else
        System.out.println ( "No");

    }
}

Python

# Simple Python code for check a matrix is
# symmetric or not.

# Fills transpose of mat[N][N] in tr[N][N]
def transpose(mat, tr, N):
    for i in range(N):
        for j in range(N):
            tr[i][j] = mat[j][i]

# Returns true if mat[N][N] is symmetric, else false
def isSymmetric(mat, N):

    tr = [ [0 for j in range(len(mat[0])) ] for i in range(len(mat)) ]
    transpose(mat, tr, N)
    for i in range(N):
        for j in range(N):
            if (mat[i][j] != tr[i][j]):
                return False
    return True

# Driver code
mat = [ [ 1, 3, 5 ], [ 3, 2, 4 ], [ 5, 4, 1 ] ]
if (isSymmetric(mat, 3)):
    print "Yes"
else:
    print "No"

# This code is contributed by Sachin Bisht

C#

// Simple C# code for check a matrix is
// symmetric or not.

using System;

class GFG {

    static int MAX = 100;

    // Fills transpose of mat[N][N] in tr[N][N]
    static void transpose(int [,]mat, int [,]tr, int N)
    {
        for (int i = 0; i < N; i++)
            for (int j = 0; j < N; j++)
                tr[i,j] = mat[j,i];
    }

    // Returns true if mat[N][N] is symmetric, else false
    static bool isSymmetric(int [,]mat, int N)
    {
        int [,]tr = new int[N,MAX];
        transpose(mat, tr, N);
        for (int i = 0; i < N; i++)
            for (int j = 0; j < N; j++)
                if (mat[i,j] != tr[i,j])
                    return false;
        return true;
    }

    // Driver code
    public static void Main ()
    {

        int [,]mat = { { 1, 3, 5 },
                        { 3, 2, 4 },
                        { 5, 4, 1 } };

        if (isSymmetric(mat, 3))
            Console.WriteLine( "Yes");
        else
            Console.WriteLine( "No");

      }
}

// This code is contributed by vt_m.

PHP

<?php
// Simple PHP code for check a matrix is
// symmetric or not.

// Returns true if mat[N][N] is
// symmetric, else false
function isSymmetric($mat, $N)
{
    $tr = array(array());
    for ($i = 0; $i < $N; $i++)
        for ($j = 0; $j < $N; $j++)
            $tr[$i][$j] = $mat[$j][$i];

    // Fills transpose of
    // mat[N][N] in tr[N][N]
    for ($i = 0; $i < $N; $i++)
        for ($j = 0; $j < $N; $j++)
            if ($mat[$i][$j] != $tr[$i][$j])
                return false;
    return true;
}

    // Driver code
    $mat= array(array(1, 3, 5),
                array(3, 2, 4),
                array(5, 4, 1));

    if (isSymmetric($mat, 3))
        echo "Yes";
    else
        echo "No";

// This code is contributed by Sam007
?>

Javascript

<script>

// Simple javascript code for check
// a matrix is symmetric or not.
let  MAX = 100;

// Fills transpose of mat[N][N] in tr[N][N]
function transpose(mat, tr, N)
{
    for(let i = 0; i < N; i++)
        for(let j = 0; j < N; j++)
            tr[i][j] = mat[j][i];
}

// Returns true if mat[N][N] is
// symmetric, else false
function isSymmetric(mat, N)
{
    let tr = new Array(N);
    for(let i = 0; i < N; i++)
    {
        tr[i] = new Array(MAX);
    }
    transpose(mat, tr, N);

    for(let i = 0; i < N; i++)
        for(let j = 0; j < N; j++)
            if (mat[i][j] != tr[i][j])
                return false;

    return true;
}

// Driver code
let mat = [ [ 1, 3, 5 ],
            [ 3, 2, 4 ],
            [ 5, 4, 1 ] ];

if (isSymmetric(mat, 3))
    document.write("Yes");
else
    document.write("No");

// This code is contributed by decode2207

</script>

Output

Yes

Time Complexity : O(N x N) 
Auxiliary Space : O(N x N)

An Efficient solution to check a matrix is symmetric or not is to compare matrix elements without creating a transpose. We basically need to compare mat[i][j] with mat[j][i].  

Implementation:

C++

// Efficient c++ code for check a matrix is
// symmetric or not.
#include <iostream>
using namespace std;

const int MAX = 100;

// Returns true if mat[N][N] is symmetric, else false
bool isSymmetric(int mat[][MAX], int N)
{
    for (int i = 0; i < N; i++)
        for (int j = 0; j < N; j++)
            if (mat[i][j] != mat[j][i])
                return false;
    return true;
}

// Driver code
int main()
{
    int mat[][MAX] = { { 1, 3, 5 },
                       { 3, 2, 4 },
                       { 5, 4, 1 } };

    if (isSymmetric(mat, 3))
        cout << "Yes";
    else
        cout << "No";
    return 0;
}

Java

// Efficient Java code for check a matrix is
// symmetric or no

import java.io.*;

class GFG {


static int MAX = 100;

// Returns true if mat[N][N]
// is symmetric, else false
 static boolean isSymmetric(int mat[][], int N)
{
    for (int i = 0; i < N; i++)
        for (int j = 0; j < N; j++)
            if (mat[i][j] != mat[j][i])
                return false;
    return true;
}

// Driver code

    public static void main (String[] args)
 {
            int mat[][] = { { 1, 3, 5 },
                    { 3, 2, 4 },
                    { 5, 4, 1 } };

    if (isSymmetric(mat, 3))
        System.out.println(  "Yes");
    else

        System.out.println("NO");

    }
}
// This article is contributed by vt_m.

Python

# Efficient Python code for check a matrix is
# symmetric or not.

# Returns true if mat[N][N] is symmetric, else false
def isSymmetric(mat, N):
    for i in range(N):
        for j in range(N):
            if (mat[i][j] != mat[j][i]):
                return False
    return True

# Driver code
mat = [ [ 1, 3, 5 ], [ 3, 2, 4 ], [ 5, 4, 1 ] ]
if (isSymmetric(mat, 3)):
    print "Yes"
else:
    print "No"

# This code is contributed by Sachin Bisht

C#

// Efficient C# code for check a matrix is
// symmetric or no

using System;

class GFG
{
    //static int MAX = 100;

    // Returns true if mat[N][N]
    // is symmetric, else false
    static bool isSymmetric(int [,]mat, int N)
    {
        for (int i = 0; i < N; i++)
            for (int j = 0; j < N; j++)
                if (mat[i, j] != mat[j, i])
                    return false;
        return true;
    }

    // Driver code
    public static void Main ()
    {
        int [,]mat = { { 1, 3, 5 },
                    { 3, 2, 4 },
                    { 5, 4, 1 } };

        if (isSymmetric(mat, 3))
            Console.WriteLine( "Yes");
        else

            Console.WriteLine("NO");

    }
}

// This code is contributed by vt_m.

PHP

<?php
// Efficient PHP code for
// check a matrix is
// symmetric or not.

$MAX = 100;

// Returns true if mat[N][N]
// is symmetric, else false
function isSymmetric($mat, $N)
{
    for ($i = 0; $i < $N; $i++)
        for ($j = 0; $j < $N; $j++)
            if ($mat[$i][$j] != $mat[$j][$i])
                return false;
    return true;
}

// Driver code
$mat = array(array(1, 3, 5),
             array(3, 2, 4),
             array(5, 4, 1));

if (isSymmetric($mat, 3))
    echo("Yes");
else
    echo("No");

// This code is contributed by Ajit.
?>

Javascript

<script>
    // Efficient Javascript code for check a matrix is symmetric or no

    let MAX = 100;

    // Returns true if mat[N][N]
    // is symmetric, else false
    function isSymmetric(mat, N)
    {
        for (let i = 0; i < N; i++)
            for (let j = 0; j < N; j++)
                if (mat[i][j] != mat[j][i])
                    return false;
        return true;
    }

    let mat = [ [ 1, 3, 5 ],
               [ 3, 2, 4 ],
               [ 5, 4, 1 ] ];

    if (isSymmetric(mat, 3))
        document.write(  "Yes");
    else

        document.write("NO");

</script>

Output

Yes

Time Complexity : O(N x N) 
Auxiliary Space : O(1)

This article is contributed by Dharmendra kumar. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.