With COMMIT or ROLLBACK statements in a trigger body, the trigger will not compile. The fail happens because triggers start during transactions. When the trigger starts the current transaction is still not complete. As COMMIT terminates a transaction, both statements (COMMIT and ROLLBACK) would lead to an exception. Changes that are executed in a trigger should be committed (or rolled back) by the owning transaction that started the trigger.

Example (Oracle):

CREATE TABLE employee_audit
(
    id          INT  NOT NULL,
    update_date DATE NOT NULL,
    old_name    VARCHAR2(100),
    new_name    VARCHAR2(100)
);

CREATE TABLE employees
(
    id   INT           NOT NULL,
    name VARCHAR2(100) NOT NULL
);

CREATE OR REPLACE TRIGGER trig_commit
    AFTER UPDATE OF name
    ON employees
    FOR EACH ROW
BEGIN
    INSERT INTO employee_audit VALUES (:old.id, SYSDATE, :old.name, :new.name);
    COMMIT;
END;

CREATE OR REPLACE TRIGGER trig_rollback
    AFTER UPDATE OF name
    ON employees
    FOR EACH ROW
BEGIN
    INSERT INTO employee_audit VALUES (:old.id, SYSDATE, :old.name, :new.name);
    ROLLBACK;
END;