Q3Multiple correct4 Marks6 Apr 2026

Let $A$ and $B$ be square matrices of the same order $n$. Which statements are sufficient to conclude that $A$ is equivalent to $B$?

A

$\det(A)=\det(B)$.

B

$\operatorname{nullity}(A)=\operatorname{nullity}(B)$.

C

The set of columns of $A$ and the set of columns of $B$ are both linearly dependent subsets of $\mathbb{R}^n$.

D

There exists a matrix $C$ such that $A$ is equivalent to $C$, and $B$ is equivalent to $C$.

E

There exist invertible matrices $P$ and $Q$ of order $n$ such that $PA=BQ$.