Help me with an SQL query..

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SQL

Hi everyone!
I have created such table:

CREATE TABLE Person
         (
             PersonID  uniqueidentifier,
             FirstName  VARCHAR(80),
             LastName   VARCHAR(100),
         );

I want to find all the persons whose lastname has no letter "a" in their lastnames. I query:

SELECT FirstName, LastName
         FROM Person
         WHERE   LastName NOT LIKE '%a%';

///// It works fine
But when i quey like that

SELECT  FirstName, LastName
         FROM   Person
         WHERE   LastName  LIKE '%[^a]%';

It doesn't work - I see the lastnames with an "a" letter....
What's the difference between these two queries??

One more question, how to select all the persons whose
last name has ONLY ONE "a" letter, ONLY TWO "a" letters, ....