1. **State the problem:** Calculate the value of the expression $3 \times 3 - 3 + 3$. 2. **Recall the order of operations:** Multiplication and division are performed before addition and subtraction. 3. **Perform the multiplication first:** $$3 \times 3 = 9$$ 4. **Substitute back into the expression:** $$9 - 3 + 3$$ 5. **Perform subtraction and addition from left to right:** $$9 - 3 = 6$$ $$6 + 3 = 9$$ 6. **Final answer:** $$9$$