Question

If $A$ is an orthogonal matrix, then $A^{-1}$ is

• A. $A$
• B. $A^{{}^{\prime }}$
• C. $A^2$
• D. None of these

Answer 1

The correct option is B $A^{{}^{\prime }}$

Since A is orthogonal matrix.
$A{A}^{\prime }=I$
On multiplying both sides by $A^{-1}$
$A^{-1}\left(A{A}^{\prime }\right)=A^{-1}I$
$\Rightarrow \left(A^{-1}A\right)A^{\prime }=A^{-1}$
$\Rightarrow \left(I\right)A^{\prime }=A^{-1}$
$\Rightarrow A^{\prime }=A^{-1}$
Option B is correct.