A is a 2 × 2 non singular matrix such that adj $A=\begin{bmatrix} sin \theta - cos \theta  & -sin\theta \, sec\theta \\2cos^2\theta & sin \theta - cos \theta \end{bmatrix}$ then |A| is :

1

The correct answer is Option (2) → 1

We know that

$|Adj\,A|=|A|^{(n-1)}$ n → order of A

$|Adj\,A|=|A|$ for n = 2

so $|Adj\,A|=|A|=(\sin θ-\cos θ)^2+\sin θ\cos^2θ\sec θ$

$=\sin^2θ+\cos^2θ-2\sin θ\cos θ+2\sin θ\cos θ$

$=1$