If U = [ ll 1 2 & -1 2 1 2 & 1 2 ], then U ^ -1 is - Vidyadip

MCQ

If $U =\left[\begin{array}{ll}\frac{1}{\sqrt{2}} & \frac{-1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}}\end{array}\right]$, then $U ^{-1}$ is

✓
$U ^{ T }$
B
U
C
I
D
$0$

✓

Answer

Correct option: A.

$U ^{ T }$

(A) $|U|=\left[\begin{array}{ll}\frac{1}{\sqrt{2}} & \frac{-1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}}\end{array}\right]=1 \neq 0$
$\therefore \quad U ^{-1}=\left[\begin{array}{ll}\frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} \\ \frac{-1}{\sqrt{2}} & \frac{1}{\sqrt{2}}\end{array}\right] \quad \ldots[$ Using Shortcut 2]
$= U ^{ T }$

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