Permutation class for my linear algebra course

permutation.py

class Permutation:
    def __init__(self, perm_list):
        self.perm_list = perm_list
        self.n = len(perm_list)
    
    def __repr__(self):
        return (
            ' '.join([str(i) for i in range(1, self.n + 1)]) +
            '\n' +
            ' '.join([str(i) for i in self.perm_list])
        )

    def power(self, p):
        perm_list = self.perm_list[:]
        
        for _ in range(p - 1):
            new_perm_list = [0] * self.n
            for i in range(self.n):
                new_perm_list[i] = perm_list[self.perm_list[i] - 1]

            self.perm_list = new_perm_list
        
        return self
    
    def inverse(self):
        new_perm_list = [0] * self.n
        for i in range(self.n):
            new_perm_list[self.perm_list[i] - 1] = i + 1
        
        self.perm_list = new_perm_list
    
        return self
    
    @staticmethod
    def mul(perm_left, perm_right):
        perm_list = [0] * perm_right.n
        for i in range(perm_right.n):
            index_for_left = perm_right.perm_list[i] - 1
            perm_res = perm_left.perm_list[index_for_left]
            perm_list[i] = perm_res
        
        return Permutation(perm_list)

    def __eq__(self, other):
        return self.perm_list == other.perm_list