Topic: Engineering Mathematics
Let $A,B\in R^{n\times n}$ be similar matrices. Which of the following is true?
- A. $det(A)=det(B)$
- B. $tr(A)=tr(B)$
- C. A, B have the same eigen values, same characteristic polynomial
- D. All of the above
Answer: D. All of the above
Explanation: Similar matrices represent the same linear transformation under two different bases, meaning there exists an invertible matrix $P$ such that $B = P^{-1}AP$. Due to this relationship, similar matrices share identical determinants, traces, eigenvalues, and characteristic polynomials.