Q21Multiple correct2 Marks16 Jul 2023

Consider the set $W=\{A\in M_n(\mathbb{R}):\det(A^T)=0\}$ with the usual addition and usual scalar multiplication of matrices. Which of the following is/are true?

A

$W$ is closed under addition.

B

$W$ is closed under scalar multiplication.

C

$W$ is a vector space.

D

$W$ is not a vector space.