Let $A = \begin{bmatrix}\cos θ&-\sin θ\\\sin θ&\cos θ\end{bmatrix}$, then $(A^{-1})^T$ equals
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $\begin{bmatrix}\cos θ&-\sin θ\\\sin θ&\cos θ\end{bmatrix}$
Let $A = \begin{bmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{bmatrix}$
This is a standard orthogonal matrix, so it satisfies: $A^{-1} = A^{T}$
Hence, $(A^{-1})^{T} = (A^{T})^{T} = A$