Let A be a 4 × 4 real matrix whose minimal polynomial is x2 + x + 1 and let B = A + I4. Which of the following statements are necessarily true?
1
The minimal polynomial of B is x2 + x + 1
2
The minimal polynomial of B is x2 - x + 1
3
B3 = I4
4
B3 + I4 = 0