GATE Civil 2023 Set 1 | Question: 37

Question

For the matrix

$$[A]=\left[\begin{array}{lll}1 & 2 & 3 \\3 & 2 & 1 \\3 & 1 & 2\end{array}\right]$$

which of the following statements is/are TRUE?

• A. The eigenvalues of $[A]^{T}$ are same as the eigenvalues of $[A]$ 
• B. The eigenvalues of $[A]^{-1}$ are the reciprocals of the eigenvalues of $[A]$ 
• C. The eigenvectors of $[A]^{T}$ are same as the eigenvectors of $[A]$ 
• D. The eigenvectors of $[A]^{-1}$ are same as the eigenvectors of $[A]$