Let A be an invertible 5 × 5 matrix over a field F. Suppose that characteristic polynomials of A and A-1 are the same.
Which of the following is necessarily true?
1
det(A)2 = 1
2
det(A)5 = 1
3
trace(A)2 = 1
4
trace (A)5 = 1
5
Question Not Attempted
Let A be an invertible 5 × 5 matrix over a field F. Suppose that characteristic polynomials of A and A-1 are the same.
Which of the following is necessarily true?