Question

For A = $\left[\begin{array}{cc}1& tanx\\ -tanx& 1\end{array}\right]$ the determinant of $A^T{A}^{-1}$ is

• A. $se{c}^{2}x$
• B. $cos4x$
• C. 1
• D. 0

Answer 1

The correct option is C 1

|A| $\ne$ 0 $\Rightarrow A^{-1}$ exits
$|A^T{A}^{-1}|=|A^T||A^{-1}|$
$=|A|\frac{1}{|A|}$
$=1$