Tisha B'Av should be spent focusing on the destruction of Jerusalem and Beit haMikdash; but is it permissible to do daily chores as well? For example, this year, Tisha B'Av is postponed one day because of Shabbos, so naturally there will be dishes to clean leftover from Shabbos. Is it permissible to do those dishes on Tisha B'Av?
The Rama (OC 553:2) writes that one should not לטייל = "take pleasure strolls" even on Erev Tisha b"Av that falls on Shabbat; how much more so must one avoid extraneous activity on Tisha b'Av itself!
The Biur Halacha there quoting the Ma'amar Mordechai drives this point home:
He concludes that despite his wishes, the prohibition on learning Torah on Tisha b'Av is the law and unfortunately cannot be altered.
The Mishna (Pesachim 4:5) states the following:
To this principle, the Tur adds (OC 554:22, 24) that this is unlikely to cause machloket (in reference to concerns voiced by the Mishna in Pesachim 4:1) - literally, ולא חיישינן ליוהרא ("and he will not be thought arrogant"). He also quotes Rabban Shimon ben Gamliel as saying that those who work on the 9th of Av will never receive a blessing (אינו רואה סימן ברכה לעולם - quoting Taanit 30b).
The Shulchan Arukh (ibid.) clarifies that latter point by saying that it is the labour they are performing that will not be blessed (אינו רואה סימן ברכה מאותה מלאכה). So far as the former principle is concerned, the following is the language of the mechaber:
The foregoing quite clearly only deals with business transactions, as is made clear in the Mishna Berurah, where it understands the stipulation that one will not see a blessing from this work as meaning that one will not see a blessing מאותן מעות שמרויח מאותה מלאכה (from the money that one gains from [doing] that work). That said, however, consider the language of the Rema (OC 554:22):
It seems to me that, based on the foregoing, you could find avenues to be both lenient or to be strict as regards the washing of dishes and the cleaning of the house. The Mishna Berurah observes that the foregoing gloss of the Rema constitutes normative halakha, so if it is your custom to rule in accordance with the Mishna Berurah, you may wish to be strict in this matter - at least until chatzot hayyom.