Q12Multiple correct4 Marks16 Mar 2025

Let $A=\begin{bmatrix}2&-3\\4&1\end{bmatrix}$. Choose all the correct options.

A

If $A$ is equivalent to a matrix $B$, then they have the same rank, trace, and determinant.

B

$B\in M_{2\times2}(\mathbb{R})$ is a matrix with the same rank, trace, and determinant as $A$. Then $A$ and $B$ are similar.

C

$B\in M_{2\times2}(\mathbb{R})$ is a matrix such that $A=\begin{bmatrix}0&-1\\5&0\end{bmatrix}B$. Then $A$ and $B$ are equivalent.

D

$A$ is equivalent to any $2\times2$ orthogonal matrix.