Q42Multiple correct2 Marks16 Oct 2022

Choose the set of correct options.

A

If there is a square matrix $A$ such that $A^2-A=0$, then $\det(A)$ must be either $0$ or $-1$.

B

If $u$ is a solution of the system of linear equations $Ax=c$ and $c$ is a solution of the system of linear equations $Ax=b$, then $u$ is a solution of the system of linear equations $A^2x=b$.

C

If $B$ is a scalar matrix of order $3$, then $AB-BA=0$ for all square matrices $A$ of order $3$.

D

If there is an invertible real $3\times3$ matrix $A$ such that $A\operatorname{adj}(A)=4I$, then $\det(\operatorname{adj}(A))$ must be $4$.