Questions: All of the statements regarding archaea are true EXCEPT - they reproduce by binary fission. - they contain a rigid cell wall. - they contain peptidoglycan in their cell walls. - they often grow in extreme environments. - they are found as single cells.

The answer is the third one: they contain peptidoglycan in their cell walls.

Explanation for each option:

1. They reproduce by binary fission.
   This statement is true. Archaea reproduce asexually through binary fission, similar to bacteria.

2. They contain a rigid cell wall.
   This statement is true. Archaea have a rigid cell wall, but it is different in composition from bacterial cell walls.

3. They contain peptidoglycan in their cell walls.
   This statement is false. Unlike bacteria, archaea do not have peptidoglycan in their cell walls. Instead, they have pseudopeptidoglycan or other unique polymers.

4. They often grow in extreme environments.
   This statement is true. Many archaea are extremophiles, thriving in environments such as hot springs, salt lakes, and deep-sea hydrothermal vents.

5. They are found as single cells.
   This statement is true. Archaea are unicellular organisms.

In summary, the incorrect statement is that archaea contain peptidoglycan in their cell walls.