Asalaam Alaikum I don't believe Islam directly says wives have to remain at home and cook/clean for their husbands. I don't believe the Quran and Hadith directly mentions this. Because women around the Muhammed's time (peace and blessings be upon him) were in a wide range of activities that occured outside their homes (like working, being in the army etc)
Islam does not specify that a woman has to cook and clean for the husband. It happens with mutual understanding. Islam does not ask the woman in specific to cook and clean for the family or even for the husband.
Our beloved Prophet Sallallahu Alaihe Wa Sallam was always helping his family during the time that he would spend in the house doing the household work.
The men should also help in the household work when their wives are doing the household work and should not consider themselves superior to the women or think that they have no responsibility in the household work.
Many things are done in the best manner in a family with the mutual understaning and mutual consultation.
And Allah knows best.
Mufti Ikram ul Haq
Fatwa Center of America
10 Jumada-al Ukhra 1432/ May 14 2011