Question:medium
If \( U = \begin{bmatrix} \frac{1}{\sqrt{2}} & -\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} \end{bmatrix} \), then \( U^{-1} \) is:
If \( U = \begin{bmatrix} \frac{1}{\sqrt{2}} & -\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} \end{bmatrix} \), then \( U^{-1} \) is:
Show Hint
Matrices involving \( 1/\sqrt{2} \) or \( \sin\theta/\cos\theta \) are frequently orthogonal. Before doing a complex inverse calculation, check if the sum of squares of the first column equals 1.
Updated On: May 1, 2026
- \( U^T \)
- \( U \)
- \( I \)
- \( 0 \)
- \( U^2 \)
Show Solution
The Correct Option is A
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