Why the Cooling fan on my car starts when I start the engine, and continues to run when I turn my car off?

I have a 2001 Impala, When I start my car, The fan goes on, Then one minute later. It goes off, Then on again, and stays on even when I turn the engine off. I changed the thermostat, and the coolant temperature sensor, and still i have the same problem. Please help.
Why the Cooling fan on my car starts when I start the engine, and continues to run when I turn my car off?
more info needed

1 most car fans run after you shut engine off..Q is does yours shut off after a while? if yes its ok/normal
Why the Cooling fan on my car starts when I start the engine, and continues to run when I turn my car off?
Your car has both a belt-driven fan and an electric fan to help cool your engine. If the thermostat and sensors are new/functioning, there might be an issue with the fan itself. If the fan keeps running when the car is off, there is a problem with the relay in the electric motor that will tell it when the car is off (your radio and air conditioning have this relay)

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