Q. $( - A)^{- 1}$ is always equal to (where $A$ is $n^{th}$ -order square matrix)
A) $( - 1)^{n}A^{- 1}$
B) $- A^{- 1}$
C) $( - 1)^{n - 1}A^{- 1}$
D) None of these
Explanation
(b)
$( - A)^{- 1} = \frac{adj( - A)}{| - A|} = \frac{( - 1)^{n - 1}adj(A)}{( - 1)^{n}|A|} = \frac{adj(A)}{- |A|} = - A^{- 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.