Determinant of a matrix (practice)

determinant.py

from itertools import permutations

def find_a_cycle(x, start):
    cycle = [start]
    s = start
    while x[s] != start:
        cycle.append(x[s])
        s = x[s]
        
    return cycle 

def find_cycles(x):
    """find cycles in a permutation of [0, 1, ..., len(x) - 1]"""
    cycles = []
    remaining = set(range(len(x)))
    
    while remaining != set():
        start = next(iter(remaining))
        cycle = find_a_cycle(x, start)
        cycles.append(cycle)
        remaining = remaining.difference(cycle)
    
    return cycles

def sgn(x):
    cycles = find_cycles(x)
    num_transpositions = sum(len(cycle) - 1 for cycle in cycles)
    return 1 if num_transpositions % 2 == 0 else -1

def det(x):
    indices = range(len(x))
    total = 0
    for perm in permutations(indices):
        value = sgn(perm)
        for i, j in zip(indices, perm):
            value *= x[i][j]
        total += value
    return total