R is a ring. Prove that J = {ab-ba | a,b in R} is an ideal of R.

To prove this, I tried proving the following things:-

1. J is nonempty. I could do this.

2. J is a subset of R. I could do this.

3. J is closed to negatives. I could do this.

4. J is closed to addition. Don't know how to do it.

5. J absorbs the products in R. I could do this.

I tried a lot but could not do #4. Could you help me? Please let me see the proof of J is closed to addition.

Alternatively, please let me know the proof of J is closed to subtraction because #3 and #4 can be clubbed into "J is closed to subtraction"

Any help?