1 1 vote Two matrices $A$ and $B$ are called similar if there exists an invertible matrix $X$ such that $A=X^{-1} B X$. Let $A$ and $B$ be two similar matrices. Consider the following statements: $\operatorname{det}(x I-A)=\operatorname{det}(x I-B)$ for any scalar $x$ The eigenvalues of $A$ and $B$ are identical $\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$ and $\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right]$ are similar Which of the following is $\text{TRUE?}$ Only statement $1$ is correct Only statement $2$ is correct Only statements $1$ and $2$ are correct All Statements $1, 2$ and $3$ are correct None of the above Linear Algebra tifrece2020 linear-algebra matrices + – admin 240 views answer comment Share Follow Add Sync Questions Print 0 reply Please log in or register to add a comment.
