Is it obligatory to wear an izaar (loincloth) when bathing alone, out of shyness before Allah?

Concealing one's nakedness in solitude is obligatory according to the majority of jurists, unless there is a need, such as bathing, relieving oneself, or removing unwanted hair. This is due to the general command to cover oneself and because Allah is most deserving of being shown modesty. The Malikis, however, have stated that covering oneself in solitude is commendable.