Hello. I wanted to ask more information about a hadith in which the Prophet, sallallaahu 'alayhi wa sallam, says that if one commits adultery, his women commit adultery too.

All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger. 

We have not come across a hadeeth with the wording that you mentioned in the question, and all the ahaadeeth that were narrated in this meaning are not authentic.

However, some scholars mentioned that many men who commit Zina (fornication or adultery) do not keep their wives chaste, so the latter [their wives] commit Zina in return – and we seek refuge in Allah from this.

Shaykh Ibn Taymiyyah said:

“If a man commits adultery, then he does not keep his wife chaste, and if she is not kept chaste (by having her desires fulfilled by her husband), she longs to have sexual intercourse with someone else other than her husband, as is generally the case with the women of the husbands who commit adultery or those who commit homosexual acts with boys. Their wives commit Zina to fulfill their desires, thus doing the same thing as their husbands out of revenge; since their husbands did not keep themselves chaste by their wives only, so in return, their wives did not keep themselves chaste by their husbands only.

It is for this reason that it was said, ‘Keep yourself chaste, your wives and your children will be chaste; be kind and dutiful to your fathers, and your children will be kind and dutiful to you.’

A person is punished by the same sin that he did, and as you treat (or deal with) others, you will be likewise treated (or dealt with) in the same manner; the punishment for a sin is another sin after it.” [End of quote from Majmoo' Al-Fataawa 15/319]

Allah knows best.