Question

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

• A. A
• B. $A^T$
• C. $A^2$
• D. none of these

Answer 1

The correct option is B $A^T$

$A$ is an orthogonal matrix.
$A{A}^T=I$
$\to A^{-1}\left(A{A}^T\right)=A^{-1}I$
$\to \left(A^{-1}A\right)A^T=A^{-1}$
$\therefore A^{-1}=A^T$