If you haven’t noticed, note that extension methods can also be called on null objects. Meaning, there can be extension method which checks whether an object is null or not. So,

public void Operate(InputType inputObject)
{
    if (null != inputObject) 
    { 
        . . .
    }
} 

public void Operate(InputType inputObject)
{
    if (null == inputObject) 
    { 
        . . .
    }
} 

Can be replaced by

public void Operate(InputType inputObject)
{
    if (inputObject.IsNotNull()) 
    { 
        . . .
    }
} 

public void Operate(InputType inputObject)
{
    if (inputObject.IsNull()) 
    { 
        . . .
    }
}