What is [\text{adj } A]^{-1} equal to?
For the following two (02) items: Let A=\begin{bmatrix}\cos~\theta&\sin~\theta\\ -\sin~\theta&\cos~\theta\end{bmatrix}
- A. -A
- B. -A^{T}
- C. A ✓
- D. A^{T}
Correct Answer: C. A
Explanation
We know the matrix identity A^{-1} = \frac{1}{|A|} \text{adj}(A). Since we calculated |A| = 1 previously, we have A^{-1} = \text{adj}(A). Therefore, [\text{adj}(A)]^{-1} = (A^{-1})^{-1} = A.
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