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 :
Answer & explanation
Correct answer: option 2
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 $|Adj\,A|=|A|=(\sin θ-\cos θ)^2+\sin θ\cos^2θ\sec θ$
$=\sin^2θ+\cos^2θ-2\sin θ\cos θ+2\sin θ\cos θ$
$=1$