A $N$x$N$ matrix is a **Toeplitz matrix** if each descending diagonal, from left to right, is constant. This means that all the elements of the diagonal are the same.

A matrix (`Mat`) is a Toeplitz matrix if Mat[i][j] is the same as Mat[i+1][j+1], Mat[i+2][j+2], and so on.

# Algorithm
For each element $[i][j]$ in our matrix, check the value of its immediate diagonal located at $[i+1][j+1]$. If we find an element whose value differs from that of its immediate diagonal, then the matrix is not a Toeplitz and we return `false`.

#include <iostream>
using namespace std;

// Matrix dimensions
#define M 4
#define N 4

// Function to determine if given matrix is Toeplitz matrix 
// or not
bool checkToepliz(int matrix[M][N])
{
	for (int i = 0; i < M - 1; i++)
		for (int j = 0; j < N - 1; j++)
			// return false if any diagonal elements have different values
			if (matrix[i][j] != matrix[i + 1][j + 1])
				return false;
	return true;
}

int main()
{
	int matrix[M][N] =
	{
		{ 3, 7, 0, 9 },
		{ 5, 3, 7, 0 },
		{ 6, 5, 3, 7 },
		{ 4, 6, 5, 3 }
	};

	if (checkToepliz(matrix))
		cout << "Is a Toepliz matrix.";
	else
		cout << "Not a Toepliz matrix.";

	return 0;
}

class ToeplizMatrix
{
	public static boolean checkToepliz(int[][] matrix)
	{
		for (int i = 0; i < matrix.length - 1; i++) {
			for (int j = 0; j < matrix[0].length - 1; j++) {
				if (matrix[i][j] != matrix[i + 1][j + 1]) {
					return false;
				}
			}
		}

		return true;
	}

	public static void main(String[] args)
	{
		int[][] matrix =
		{
			{ 3, 7, 0, 9 },
			{ 5, 3, 7, 0 },
			{ 6, 5, 3, 7 },
			{ 4, 6, 5, 3 }
		};

		if (checkToepliz(matrix)) {
			System.out.print("Is a Toepliz matrix");
		}
		else {
			System.out.print("Not a Toepliz matrix");
		}
	}
}

Java

N = 4
M = 4

# Function to check whether given   
# matrix is a Toeplitz matrix or not 
def isToeplitz(mat):  
	for i in range(0, N-1): 
		for j in range(M-1): 
			if (mat[i][j]!=mat[i+1][j+1]):
				return False
    
	return True
  
# Driver Code  
if __name__ == "__main__": 
          
    mat = [[6, 7, 8, 9], 
          [4, 6, 7, 8], 
          [1, 4, 6, 7], 
          [0, 1, 4, 6], 
          [2, 0, 1, 4]] 
  
    if(isToeplitz(mat)): 
        print("Is a Toeplitz matrix") 
    else: 
        print("Not a Toeplitz matrix") 

Python

How to check if a given matrix is a Toeplitz matrix 

A NNNxNNN matrix is a Toeplitz matrix if each descending diagonal, from left to right, is constant. This means that all the elements of the diagonal are the same. A matrix (Mat) is a Toeplitz matrix if Mat[i][j] is the same as Mat[i+1][j+1], Mat[i+2][j+2], and so on. Algorithm For each element [i][j][i][j][i][j] in our matrix, check the value of its immediate diagonal located at [i+1][j+1][i+1][j+1][i+1][j+1]. If we find an element whose value differs from that of its immediate diagonal, then the matrix is not a Toeplitz and we return false. 

How to check if a given matrix is a Toeplitz matrix

Algorithm

Implementation