Q. If $A$ is a $3 \times 3$non-singular matrix, then det $\left( A^{- 1}adj\ A \right)$ is equal to
A) $\det A$
B) 1
C) $\left( \det A \right)^{2}$
D) $\left( \det A \right)^{- 1}$
Explanation
(a)
$\det\left( A^{- 1}adj\ A \right) = \det\left( A^{- 1} \right)det(adj\ A)$
${= (det}{{A)}^{- 1}(\det{A)^{3 - 1} = \det A}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.