Q. If $A$ is an orthogonal matrix, then $A^{- 1}$equals
A) $A^{T}$
B) $A$
C) $A^{2}$
D) None of these
Explanation
(a)
$A \times A^{T} = I$
$\Rightarrow \ \left| A \times A^{T} \right| = |I|$
$\Rightarrow |A|^{2} = 1$
$\Rightarrow |A| = \pm 1$
$\Rightarrow A^{- 1}$ exists
$\Rightarrow A^{- 1} \times A \times A^{T} = A^{- 1} \times I$
$\Rightarrow A^{- 1} = A^{T}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.