jee-main 2022 Q70

jee-main · India · session2_29jul_shift1 Matrices Linear Transformation and Endomorphism Properties
Let $A$ and $B$ be two $3 \times 3$ non-zero real matrices such that $A B$ is a zero matrix. Then
(1) The system of linear equations $A X = 0$ has a unique solution
(2) The system of linear equations $A X = 0$ has infinitely many solutions
(3) $B$ is an invertible matrix
(4) $\operatorname { adj } ( A )$ is an invertible matrix
Let $A$ and $B$ be two $3 \times 3$ non-zero real matrices such that $A B$ is a zero matrix. Then\\
(1) The system of linear equations $A X = 0$ has a unique solution\\
(2) The system of linear equations $A X = 0$ has infinitely many solutions\\
(3) $B$ is an invertible matrix\\
(4) $\operatorname { adj } ( A )$ is an invertible matrix