# Find if given matrix is Toeplitz or not in C++

In this problem, we are given a 2D square matrix mat[][] of size n*n. Our task is to find if the given matrix is Toeplitz or not.

Toeplitz matrix also known as diagonal matrix is a matrix in which the elements at the diagonal start from top-left corner to bottom-right corner.

## Let’s take an example to understand the problem,

Input:

Mat[][] = {{3, 5, 1},
{4, 3 ,2},
{1, 2, 3}}

Output: Yes

Explanation:

Diagonal : (0, 0), (1, 1) , (2, 2) has the same value 3.

Solution Approach:

A simple approach to solve the problem is checking all the elements at a diagonal index. These diagonal values will be indexes where the value of both i and j is the same.

So, we need to check for all i -> 0 to n and j -> 0 to n. If i = j, and mat[i][j] is the same for all.

## Example

Live Demo

#include <iostream>
using namespace std;
#define N 4

bool isToeplizMatrix(int mat[N][N])
{
int diagVal = mat;
for(int i = 0; i < N ; i++)
{
if(mat[i][i] != diagVal){
return false;
}
}
return true;
}

int main(){

int mat[N][N] = { { 6, 7, 8, 9 },
{ 4, 6, 7, 8 },
{ 1, 4, 6, 7 },
{ 0, 1, 4, 6 }};

if (isToeplizMatrix(mat))
cout<<"Matrix is a Toepliz matrix.";
else
cout<<"Matrix is not a Toepliz matrix.";

return 0;
}

## Output

Matrix is a Toepliz matrix.