from datetime import date
from calendar import monthrange


def date_a_month_ago(today):
    x = today.month - 1
    previous_month = 12 if x == 0 else x
    year = today.year - 1 if x == 0 else today.year
    last_day_of_previous_month = monthrange(year, previous_month)[1]
    day = last_day_of_previous_month if today.day > last_day_of_previous_month else today.day
    return date(year, previous_month, day)


# Tests
print(date_a_month_ago(date(2021, 11, 1)))
print(date_a_month_ago(date(2021, 1, 31)))
print(date_a_month_ago(date(2021, 12, 31)))
print(date_a_month_ago(date(2021, 3, 29)))
print(date_a_month_ago(date(2020, 3, 29)))
print(date_a_month_ago(date(2021, 3, 30)))
print(date_a_month_ago(date(2020, 3, 30)))