For the following two (02) items: Let A = pmatrix θ & θ - θ & θ...

Given $A = \begin{pmatrix} \cos\theta & \sin\theta \\ -\sin\theta & \cos\theta \end{pmatrix}$

The determinant of $A$ is $|A| = \cos^2\theta - (-\sin\theta)(\sin\theta) = \cos^2\theta + \sin^2\theta = 1$

For any non-singular matrix, the inverse is given by $A^{-1} = \dfrac{1}{|A|} \text{adj}\, A$

Substituting $|A| = 1$, we get $\text{adj}\, A = A^{-1}$

Taking the inverse on both sides yields $[\text{adj}\, A]^{-1} = (A^{-1})^{-1} = A$

Answer: $A$