Intersecting Rows and Columns

Suppose any nxm matrix of 0s and 1s can be transformed into a second matrix, where each number in position (i, j) in the new matrix is the sum of 1s in row i and column j in the original matrix, excluding itself (if it is a 1).

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

[1, 5, 2, 4, 1],
[2, 4, 1, 3, 2],
[2, 4, 1, 1, 2],
[3, 2, 2, 2, 3],
[2, 2, 1, 3, 2]
# The 1 on the upper left corner has 1 other 1 in the same row as itself (excluding itself).
# The 0 to the right of the 1 has 2 1's on the same row as itself, and 3 1's in the same column, etc.

Create a function that transforms the first matrix into its second matrix equivalent.

Examples

transform_matrix([
  [1, 0, 0],
  [0, 1, 0],
  [0, 0, 1]
]) ➞ [
  [0, 2, 2],
  [2, 0, 2],
  [2, 2, 0]
]

transform_matrix([
  [1, 1, 1],
  [0, 0, 1],
  [0, 0, 1]
]) ➞ [
  [2, 2, 4],
  [2, 2, 2],
  [2, 2, 2]
]

transform_matrix([
  [1, 1, 1],
  [0, 1, 1],
  [0, 0, 1]
]) ➞ [
  [2, 3, 4],
  [3, 2, 3],
  [2, 3, 2]
]

Notes

It might be easier to visualize this by drawing the grid of 0's and 1's out on a sheet of paper, and drawing lines through a specific number's row and column.