Q. If $A$ and $B$ are squares matrices such that $A^{2006} = O$and $AB = A + B,$ then det$(B)$ equals
A) 0
B) 1
C) $- 1$
D) None of these
Explanation
(a)
$AB = A + B$
$\Rightarrow B = AB - A = A(B - I)$
$\Rightarrow$det$(B) = \det(A)\det(B - I) = 0$
$\Rightarrow$det $(B) = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.