Recursive DFS function that looks if a position in a binary matrix has a 1 and all other elements in its row and column have 0

Question

I'm working on LeetCode 1582. Special Positions in a Binary Matrix. How could I make a function that uses recursion and DFS to return the count of how many special positions are in a m x n binary matrix. A position (i, j) is called special if matrix[i][j] == 1 and all other elements in row i and column j are 0 (rows and columns are 0-indexed).

Example 1

Input: mat = [[1,0,0],[0,0,1],[1,0,0]]
Output: 1
Explanation: (1, 2) is a special position because mat[1][2] == 1 and all other elements in row 1 and column 2 are 0.

Example 2

Input: mat = [[1,0,0],[0,1,0],[0,0,1]]
Output: 3
Explanation: (0, 0), (1, 1) and (2, 2) are special positions.

This is what I have so far, but I am stumped on how to correctly execute the DFS recursion given this problem.

class Solution:
    def numSpecial(self, mat: List[List[int]]) -> int:
        count = 0
        for ir, rval in enumerate(mat):
            for ic, cval in enumerate(rval):
                if cval == 1:
                    if self.dfs([ir, ic], mat):
                        count += 1
        return count

                        
    def dfs(self, idx, mat):
        if self.isvalid(idx, mat):
            if mat[idx[0]][idx[1]] != 0:
                return False
            else:
                north = [idx[0]-1, idx[1]]
                self.dfs(north)
                south = [idx[0]+1, idx[1]]
                self.dfs(south)
                east = [idx[0], idx[1]+1]
                self.dfs(east)
                west = [idx[0], idx[1]-1]
                self.dfs(west)
                return True # dont know if and where I should put this return True
        
    
    def isvalid(self, idx, mat):
        if idx[0] in range(0,len(mat)):
            if idx[1] in range(0,len(mat[0])):
                return True
        return False
        

Also, I understand that there are many simpler ways to solve this problem, but I just want to be able to solve it using DFS recursion like how I was attempting to above