Check if Matrix Is X-Matrix

Easy

Problem

A square matrix is said to be an X-Matrix if both of the following conditions hold:

All the elements in the diagonals of the matrix are non-zero.
All other elements are 0.

Given a 2D integer array grid of size n x n representing a square matrix, return true if grid is an X-Matrix. Otherwise, return false.

Constraints

n == grid.length == grid[i].length
3 <= n <= 100
0 <= grid[i][j] <= 10^5

Examples

Input: grid = [[2,0,0,1],[0,3,1,0],[0,5,2,0],[4,0,0,2]]

Output: true

The diagonal elements (positions where i == j or i + j == n - 1) are all non-zero: 2, 1, 3, 1, 5, 2, 4, 2. All other elements are 0. Thus, grid is an X-Matrix.

Input: grid = [[5,7,0],[0,3,1],[0,5,0]]

Output: false

The element at position (0,1) is 7, which should be 0 since it's not on a diagonal. Also, position (1,2) is 1 instead of 0. Thus, grid is not an X-Matrix.

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