Is it permissible to tell one's wife about good deeds to encourage her, and is that considered showing off (riya') that nullifies the reward?

The more a deed is hidden, the closer it is to sincerity and the further it is from ostentation. Secret charity extinguishes the Lord's wrath, and one who recites the Qur'an secretly is better than one who recites it openly, to be safe from conceit.

However, it is permissible to display good deeds if there is a legitimate benefit, such as people emulating them and being encouraged to do good, provided it is free from ostentation and seeking fame. Allah has praised both giving charity openly and secretly, but He praised secrecy for its safety from the affliction of ostentation.

If displaying a deed encourages people to emulate and follow, especially for someone who is knowledgeable and righteous, then displaying it is better; because its benefit extends to others and for the reward associated with initiating a good practice. But if this condition is not met, then secrecy is better. A believer should consider what is most beneficial and advantageous for their heart and for Islam and Muslims. There is no harm in informing one's wife about some good deeds to encourage her to follow suit, while maintaining sincerity in the deed for Allah.