TIFR ECE 2015 | Question: 6

Question

$\textbf{A}$ is an $n \times n$ square matrix of reals such that $\mathbf{A y}=\mathbf{A}^{T} \mathbf{y}$, for all real vectors $\mathbf{y}$. Which of the following can we conclude?

1. $\mathbf{A}$ is invertible
2. $\mathbf{A}^{T}=\mathbf{A}$
3. $\mathbf{A}^{2}=\mathbf{A}$

 

• A. Only (i)
• B. Only (ii)
• C. Only (iii)
• D. Only (i) and (ii)
• E. None of the above