Math 3191 Extra Homework #2

1. If

calculate the following:

How do these results compare with the same expressions where A, B and I are numbers? (I=1)

For problems 2-4: Two matrices A and B are said to commute if AB = BA.

2. Describe all 2 by 2 matrices that commute with .

. (Hint: Let and consider AB - BA = 0.)

3. Describe all 3 by 3 matrices that commute with .

4. Describe all 3 by 3 matrices that commute with .