# Program to check if matrix is lower triangular

Given a square matrix and the task is to check the matrix is in lower triangular form or not. A square matrix is called lower triangular if all the entries above the main diagonal are zero.

Examples:

```Input : mat[4][4] = {{1, 0, 0, 0},
{1, 4, 0, 0},
{4, 6, 2, 0},
{0, 4, 7, 6}};
Output : Matrix is in lower triangular form.

Input : mat[4][4] = {{1, 0, 0, 0},
{4, 3, 0, 1},
{7, 9, 2, 0},
{8, 5, 3, 6}};
Output : Matrix is not in lower triangular form.```

Implementation:

## C++

 `// Program to check lower ``// triangular matrix. ``#include ``#define N 4 ``using` `namespace` `std; `` ` `// Function to check matrix is in  ``// lower triangular form or not. ``bool` `isLowerTriangularMatrix(``int` `mat[N][N]) ``{ ``    ``for` `(``int` `i = 0; i < N-1; i++) ``        ``for` `(``int` `j = i + 1; j < N; j++) ``            ``if` `(mat[i][j] != 0) ``                ``return` `false``; ``    ``return` `true``; ``} `` ` `// Driver function. ``int` `main() ``{ ``    ``int` `mat[N][N] = { { 1, 0, 0, 0 }, ``                      ``{ 1, 4, 0, 0 }, ``                      ``{ 4, 6, 2, 0 }, ``                      ``{ 0, 4, 7, 6 } }; `` ` `    ``// Function call ``    ``if` `(isLowerTriangularMatrix(mat)) ``        ``cout << ``"Yes"``; ``    ``else``        ``cout << ``"No"``; ``    ``return` `0; ``} `

## Java

 `// Java Program to check for  ``// a lower triangular matrix. ``import` `java.io.*; `` ` `class` `Lower_triangular ``{ ``    ``int` `N = ``4``; `` ` `    ``// Function to check matrix is  ``    ``// in lower triangular form or not. ``    ``boolean` `isLowerTriangularMatrix(``int` `mat[][]) ``    ``{ ``        ``for` `(``int` `i = ``0``; i < N-``1``; i++) ``            ``for` `(``int` `j = i + ``1``; j < N; j++) ``                ``if` `(mat[i][j] != ``0``) ``                    ``return` `false``; `` ` `        ``return` `true``; ``    ``} `` ` `    ``// Driver function. ``    ``public` `static` `void` `main(String args[]) ``    ``{ ``        ``Lower_triangular ob = ``new` `Lower_triangular(); ``        ``int` `mat[][] = { { ``1``, ``0``, ``0``, ``0` `}, ``                        ``{ ``1``, ``4``, ``0``, ``0` `}, ``                        ``{ ``4``, ``6``, ``2``, ``0` `}, ``                        ``{ ``0``, ``4``, ``7``, ``6` `} }; ``                         ` `        ``// Function call ``        ``if` `(ob.isLowerTriangularMatrix(mat)) ``            ``System.out.println(``"Yes"``); ``        ``else``            ``System.out.println(``"No"``); ``    ``} ``} `` ` `// This code is contributed by Anshika Goyal. `

## Python3

 `# Python3 Program to check  ``# lower triangular matrix. `` ` `# Function to check matrix  ``# is in lower triangular ``def` `islowertriangular(M): ``    ``for` `i ``in` `range``(``0``, ``len``(M)): ``        ``for` `j ``in` `range``(i ``+` `1``, ``len``(M)): ``            ``if``(M[i][j] !``=` `0``):  ``                    ``return` `False``    ``return` `True``     ` `# Driver function. ``M ``=` `[[``1``,``0``,``0``,``0``], ``     ``[``1``,``4``,``0``,``0``], ``     ``[``4``,``6``,``2``,``0``], ``     ``[``0``,``4``,``7``,``6``]] `` ` `if` `islowertriangular(M): ``    ``print` `(``"Yes"``) ``else``: ``    ``print` `(``"No"``) ``     ` `# This code is contributed by Anurag Rawat `

## C#

 `// C# program to check for ``// a lower triangular matrix. ``using` `System; `` ` `class` `Lower_triangular  ``{ ``    ``int` `N = 4; `` ` `    ``// Function to check matrix is ``    ``// in lower triangular form or not. ``    ``bool` `isLowerTriangularMatrix(``int``[, ] mat) ``    ``{ ``        ``for` `(``int` `i = 0; i < N; i++) ``            ``for` `(``int` `j = i + 1; j < N; j++) ``                ``if` `(mat[i, j] != 0) ``                    ``return` `false``; `` ` `        ``return` `true``; ``    ``} `` ` `    ``// Driver function. ``    ``public` `static` `void` `Main() ``    ``{ ``        ``Lower_triangular ob = ``new` `Lower_triangular(); ``        ``int``[, ] mat = { { 1, 0, 0, 0 }, ``                        ``{ 1, 4, 0, 0 }, ``                        ``{ 4, 6, 2, 0 }, ``                        ``{ 0, 4, 7, 6 } }; `` ` `        ``// Function call ``        ``if` `(ob.isLowerTriangularMatrix(mat)) ``            ``Console.WriteLine(``"Yes"``); ``        ``else``            ``Console.WriteLine(``"No"``); ``    ``} ``} `` ` `// This code is contributed by vt_m. `

## PHP

 ` `

## Javascript

 ` `

Output
`Yes`

Time Complexity: O(n2), where n represents the number of rows and columns of the matrix.
Auxiliary Space: O(1), no extra space is required, so it is a constant.

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