Question

If A is an orthogonal matrix of order n, then the value of |adj.(adj A)| is

• A. $0$
• B. $\pm 1$
• C. $n$
• D. $n-2$

Answer 1

The correct option is B $\pm 1$

$A{A}^{\prime }=I\Rightarrow |A|=\pm 1\therefore |adj.(adj.A)|=|A{|}^{(n-1{)}^2}=\pm 1.$