Is it common for people with Alzhiemer's to be able to do one task but not the reverse of it?
There can be many things going on here. The person may not be able to understand the function of an item anymore -- so she looks at an object, but can no longer readily identify it. If she doesn't recognize a faucet or an article of clothing, she may not be able to figure out what to do with it. Another possibility is that a person may turn water on or unlock a door by accident when she is simply touching things and fooling around with them. When this happens, it's unlikely she will figure out how to reverse the action. This doesn't always happen in people with Alzheimer’s, but it's not uncommon; it depends on what areas of the brain are damaged.
There can also be physical problems that are interfering with functioning, such as arthritis, stiffness, or lack of fine motor skills that are making it physically difficult to manipulate objects.