TIFR ECE 2012 | Question: 17

Question

Let $A=U \Lambda U^{\dagger}$ be a $n \times n$ matrix, where $U U^{\dagger}=I$. Which of the following statements is TRUE.

• A. The matrix $I+A$ has non-negative eigen values
• B. The matrix $I+A$ is symmetic
• C. $\operatorname{det}(I+A)=\operatorname{det}(I+\Lambda)$
• D. $(a)$ and $(c)$
• E. $(b)$ and $(c)$
• F. $(a), (b)$ and $(c)$