Question

If $A$ is an orthogonal matrix & $|A|=1$, then $A^T$ is equal to

• A. $-A$
• B. $A$
• C. $-\left(adjA\right)$
• D. $\left(adj\right)A$

Answer 1

The correct option is D $\left(adj\right)A$

$A$ is an orthogonal matrix and $|A|=1$

$A{A}^{\prime }=I$$\Rightarrow A^{\prime }=A^{-1}$

$\therefore A^{\prime }=A^{-1}=\frac{adjA}{|A|}=adjA$

Hence, option D.