If A = [ cc i & 0 0 & i 2 ] where ( i =-1), then A ^ -1 = - Vidyadip

MCQ

If $A =\left[\begin{array}{cc} i & 0 \\ 0 & \frac{ i }{2}\end{array}\right]$ where $( i =\sqrt{-1})$, then $A ^{-1}=$

A
$\left[\begin{array}{ll} i & 0 \\ 0 & \frac{ i }{2}\end{array}\right]$
✓
$\left[\begin{array}{cc}- i & 0 \\ 0 & -2 i \end{array}\right]$
C
$\left[\begin{array}{cc} i & 0 \\ 0 & 2 i \end{array}\right]$
D
$\left[\begin{array}{cc}0 & i \\ 2 i & 0\end{array}\right]$

✓

Answer

Correct option: B.

$\left[\begin{array}{cc}- i & 0 \\ 0 & -2 i \end{array}\right]$

(B) $|A|=-\frac{1}{2} \neq 0$
$\therefore \quad A ^{-1}=\frac{1}{\frac{-1}{2}}\left[\begin{array}{ll}\frac{ i }{2} & 0 \\ 0 & i \end{array}\right]=\left[\begin{array}{cc}- i & 0 \\ 0 & -2 i \end{array}\right]$ ...[Using Shortcut 2]

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