Q. If $n^{th}$-order square matrix $A$is a orthogonal, then, $\left| adj(adj\ A) \right|$ is
A) Always $- 1$ if $n$ is even
B) Always 1 if $n$ is odd
C) Always 1
D) None of these
Explanation
(b)
Since $A$ is orthogonal, hence
$AA^{T} = I$
$\Rightarrow \left| AA^{T} \right| = 1$
$\Rightarrow \left| A^{2} \right| = 1$
$\Rightarrow |A| = = \pm 1$
Now, $\left| adj(adj\ A) \right| = |A|^{(n - 1)^{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.