jee-main 2023 Q68

jee-main · India · session1_24jan_shift1 Matrices Matrix Algebra and Product Properties
If $A$ and $B$ are two non-zero $n \times n$ matrices such that $A ^ { 2 } + B = A ^ { 2 } B$, then
(1) $A B = I$
(2) $A ^ { 2 } B = I$
(3) $A ^ { 2 } = I$ or $B = I$
(4) $A ^ { 2 } B = B A ^ { 2 }$
If $A$ and $B$ are two non-zero $n \times n$ matrices such that $A ^ { 2 } + B = A ^ { 2 } B$, then\\
(1) $A B = I$\\
(2) $A ^ { 2 } B = I$\\
(3) $A ^ { 2 } = I$ or $B = I$\\
(4) $A ^ { 2 } B = B A ^ { 2 }$