Math 3191 Extra Homework #2

calculate the following:

• a) A^2B^2 - (AB)^2
• b) ABA - BA^2
• c) A^2 + 2A + I - (A + I)^2
• d) A^2 - 3I
• e) (A^2 - 3I)^2
• f) A^4 - 6A^2 + 9I

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 .