Q. If $P$ is non-singular matrix, then value of adj$(P^{- 1})$ in terms of $P$ is
A) $\frac{P}{|P|}$
B) $P|P|$
C) $P$
D) None of these
Explanation
(a)
We know that for any non-singular matrix $A$,
$A^{- 1} = \frac{1}{|A|}adj(A)$
Now put $A = P^{- 1}$. Then we have
$\left( P^{- 1} \right)^{- 1} = \frac{1}{\left| P^{- 1} \right|}adj\left( P^{- 1} \right)$
$\Rightarrow P = |P|adj(P^{- 1})$
$\Rightarrow adj\left( P^{- 1} \right) = \frac{P}{|P|}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.