Q26Multiple correct3 Marks3 Dec 2023

Let $A$ and $B$ be $n\times n$ matrices. Which statements are true?

A

If $A$ and $B$ are similar, then the nullity of $A$ and the nullity of $B$ are equal.

B

Let $A$ and $B$ be similar matrices. Then $Ax=0$ has a unique solution if and only if $Bx=0$ has a unique solution.

C

If $A^k$ and $B^k$ are similar for some positive integer $k$, then $A$ and $B$ are similar.

D

If $A$ and $B$ are similar matrices where $A$ is a scalar matrix, then $A=B$.