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# 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 ``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

 ``

## Javascript

 ``

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 ``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

 ``

## Javascript

 ``

Output

`Yes`

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

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