Q34Multiple correct2 Marks20 Nov 2022

Which of the following options are true?

A

Every matrix is similar to itself.

B

If $A$ is similar to $B$, then $A^{-1}$ is similar to $B^{-1}$.

C

$\begin{bmatrix}2&1\\0&2\end{bmatrix}$ is similar to $\begin{bmatrix}2&0\\0&2\end{bmatrix}$.

D

If $A$ is similar to $B+C$, then $\operatorname{rank}(A)=\operatorname{rank}(B)+\operatorname{rank}(C)$.