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Maximum determinant of a matrix with every values either 0 or n
• Difficulty Level : Easy
• Last Updated : 30 Nov, 2018

We have given a positive number n, and we have to find a 3*3 matrix which can be formed with combination of 0 or n and has maximum determinant.

Examples :

```Input : n = 3
Output : Maximum determinant = 54
Resultant Matrix :
3 3 0
0 3 3
3 0 3

Input : n = 13
Output : Maximum determinant = 4394
Resultant Matrix :
13 13  0
0  13 13
13  0 13
```

Explanation:
For any 3*3 matrix having elements either 0 or n, the maximum possible determinant is 2*(n^3).. Also a matrix having maximum determinant is of form:
n n 0
0 n n
n 0 0

## C++

 `// C++ program to find  maximum possible determinant``// of 0/n matrix.``#include ``using` `namespace` `std;`` ` `// Function for maximum determinant``int` `maxDet(``int` `n)``{``    ``return` `(2*n*n*n);``}`` ` `// Function to print resulatant matrix``void` `resMatrix ( ``int` `n)``{``    ``for` `(``int` `i = 0; i < 3; i++)``    ``{``        ``for` `(``int` `j = 0; j < 3; j++)``        ``{``            ``// three position where 0 appears``            ``if` `(i == 0 && j == 2)``                ``cout << ``"0 "``;``            ``else` `if` `(i == 1 && j == 0)``                ``cout << ``"0 "``;``            ``else` `if` `(i == 2 && j == 1)``                ``cout << ``"0 "``;`` ` `            ``// position where n appears``            ``else``                ``cout << n << ``" "``;``        ``}``        ``cout << ``"\n"``;``    ``}``} `` ` `// Driver code``int` `main()``{``    ``int` `n = 15;``    ``cout << ``"Maximum Determinant = "` `<< maxDet(n);`` ` `    ``cout << ``"\nResultant Matrix :\n"``;``    ``resMatrix(n); `` ` `    ``return` `0;``}`

## Java

 `// Java program to find maximum possible``// determinant of 0/n matrix.``import` `java.io.*;`` ` `public` `class` `GFG``{``     ` `// Function for maximum determinant``static` `int` `maxDet(``int` `n)``{``    ``return` `(``2` `* n * n * n);``}`` ` ` ` `// Function to print resulatant matrix``void` `resMatrix(``int` `n)``{``    ``for` `(``int` `i = ``0``; i < ``3``; i++)``    ``{``        ``for` `(``int` `j = ``0``; j < ``3``; j++)``        ``{``            ``// three position where 0 appears``            ``if` `(i == ``0` `&& j == ``2``)``                ``System.out.print(``"0 "``);``            ``else` `if` `(i == ``1` `&& j == ``0``)``                ``System.out.print(``"0 "``);``            ``else` `if` `(i == ``2` `&& j == ``1``)``                ``System.out.print(``"0 "``);`` ` `            ``// position where n appears``            ``else``                ``System.out.print(n +``" "``);``        ``}``        ``System.out.println(``""``);``    ``}``} `` ` `    ``// Driver code``    ``static` `public` `void` `main (String[] args)``    ``{``            ``int` `n = ``15``;``            ``GFG geeks=``new` `GFG();``            ``System.out.println(``"Maximum Determinant = "``                                ``+ maxDet(n));`` ` `            ``System.out.println(``"Resultant Matrix :"``); ``            ``geeks.resMatrix(n); `` ` `    ``}``}`` ` `// This code is contributed by vt_m.`

## Python3

 `# Python 3 program to find maximum``# possible determinant of 0/n matrix. ``# Function for maximum determinant``def` `maxDet(n):``    ``return` `2` `*` `n ``*` `n ``*` `n`` ` `# Function to print resulatant matrix ``def` `resMatrix(n):``    ``for` `i ``in` `range``(``3``):``        ``for` `j ``in` `range``(``3``):`` ` `            ``# three position where 0 appears``            ``if` `i ``=``=` `0` `and` `j ``=``=` `2``:``                ``print``(``"0"``, end ``=` `" "``)``            ``elif` `i ``=``=` `1` `and` `j ``=``=` `0``:``                ``print``(``"0"``, end ``=` `" "``)``            ``elif` `i ``=``=` `2` `and` `j ``=``=` `1``:``                ``print``(``"0"``, end ``=` `" "``)`` ` `            ``# position where n appears``            ``else``:``                ``print``(n, end ``=` `" "``)``        ``print``(``"\n"``)``         ` `# Driver code``n ``=` `15``print``(``"Maximum Detrminat="``, maxDet(n))``print``(``"Resultant Matrix:"``)``resMatrix(n)`` ` `# This code is contributed by Shrikant13`

## C#

 `// C# program to find maximum possible``// determinant of 0/n matrix.``using` `System;`` ` `public` `class` `GFG``{``     ` `// Function for maximum determinant``static` `int` `maxDet(``int` `n)``{``    ``return` `(2 * n * n * n);``}`` ` ` ` `// Function to print resulatant matrix``void` `resMatrix(``int` `n)``{``    ``for` `(``int` `i = 0; i < 3; i++)``    ``{``        ``for` `(``int` `j = 0; j < 3; j++)``        ``{``            ``// three position where 0 appears``            ``if` `(i == 0 && j == 2)``                ``Console.Write(``"0 "``);``            ``else` `if` `(i == 1 && j == 0)``                ``Console.Write(``"0 "``);``            ``else` `if` `(i == 2 && j == 1)``                ``Console.Write(``"0 "``);`` ` `            ``// position where n appears``            ``else``                ``Console.Write(n +``" "``);``        ``}``        ``Console.WriteLine(``""``);``    ``}``} `` ` `    ``// Driver code``    ``static` `public` `void` `Main (String []args)``    ``{``            ``int` `n = 15;``            ``GFG geeks=``new` `GFG();``            ``Console.WriteLine(``"Maximum Determinant = "``                                ``+ maxDet(n));`` ` `            ``Console.WriteLine(``"Resultant Matrix :"``); ``            ``geeks.resMatrix(n); `` ` `    ``}``}`` ` `// This code is contributed by vt_m.`

## PHP

 ``

Output :

```Maximum Determinant = 6750
Resultant Matrix :
15 15  0
0  15 15
15 0  15
```

Exercise: Extend the above solution for a generalized k x k matrix.

This article is contributed by Shivam Pradhan (anuj_charm). If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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