Q. Suppose A and B are nxn invertible matrices, where n>1 and I is the identity nxn matrix. If A and B are similar matrices, which of the following are true?
I. A-2I and B-2I are similar matrices
II. A and B have the same trace
III. A^-1 and B^-1 are similar matrices
(A)I only (B) II only (C) III only (D) I & III only (E) I,II,III
The answer is E. I get that II is true. I know similar matrices share alot of properties but can someone prove both I and III.
Again, thanks in advance,