No Intersecting Ones

A no-intersecting ones matrix is one where no two ones exist on the same row or column.

To illustrate:

[
  [1, 0, 0, 0, 0],
  [0, 1, 0, 0, 0],
  [0, 0, 0, 1, 0],
  [0, 0, 0, 0, 0],
  [0, 0, 1, 0, 0]
]

The list below is not a non-intersecting ones matrix:

[
  [1, 0, 0, 0, 0],
  [0, 1, 0, 0, 0],
  [0, 0, 0, 1, 0],
  [0, 1, 0, 0, 0],
  [0, 0, 0, 0, 0]
]

// Column 2 has two 1s.

Write a function that returns True if a 2D matrix is a no-intersecting ones matrix and False otherwise.

Examples

no_intersecting_nes([
  [0, 1],
  [1, 0]
]) ➞ True

no_intersecting_ones([
  [1, 1],
  [0, 0]
]) ➞ False

no_intersecting_ones([
  [0, 0, 0, 1],
  [1, 0, 0, 0],
  [0, 1, 0, 0]
]) ➞ True

Notes

N/A