Question

Let \(A = \left[ \begin{array}{ccc}cosα & -sinα & 0 \\ sinα & cosα & 0 \\ 0 & 0 & 1\end{array} \right]\). If \(B = \text{adj}\,A\), then the matrix \(B^{-1}\) is equal to...

• A. \(I\)
• B. \(A^{-1}\)
• C. \(-A\)
• D. \(A\)

Hint:

For a matrix with determinant 1, the adjoint equals the inverse.

Answer 1

The Correct Option is D

Step 1: Use the general identity:
$\text{adj}(A) = |A| A^{-1}$, so $(\text{adj}A)^{-1} = \frac{A}{|A|}$.

Step 2: Substitute:
Since $|A| = 1$, $B^{-1} = A$.

Final Answer:
$B^{-1} = A$, option (D). \[ \boxed{A} \]