The statement is False. While archaea do exhibit a variety of methods for genetic exchange, such as horizontal gene transfer, they primarily reproduce asexually through a process called binary fission. In binary fission, a single archaeal cell divides into two identical daughter cells, allowing for rapid population growth.
Although there are some studies suggesting certain forms of genetic recombination that may resemble sexual reproduction, true sexual reproduction with gametes and mating types, as seen in animals or plants, does not occur in archaea. Their methods of genetic exchange do not equate to sexual reproduction as defined in more complex organisms. So, while they can exchange genetic material, it does not fit the traditional definition of sexual reproduction.