If A = [ * 20 c i&0 0& i/2 ] (i = - 1 ),then A^ - 1 = - Vidyadip

MCQ

If $A = \left[ {\begin{array}{*{20}{c}}i&0\\0&{i/2}\end{array}} \right]$ $(i = \sqrt { - 1} ),$then ${A^{ - 1}}$=

A
$\left[ {\begin{array}{*{20}{c}}i&0\\0&{i/2}\end{array}} \right]$
✓
$\left[ {\begin{array}{*{20}{c}}{ - i}&0\\0&{ - 2i}\end{array}} \right]$
C
$\left[ {\begin{array}{*{20}{c}}i&0\\0&{2i}\end{array}} \right]$
D
$\left[ {\begin{array}{*{20}{c}}0&i\\{2i}&0\end{array}} \right]$

✓

Answer

Correct option: B.

$\left[ {\begin{array}{*{20}{c}}{ - i}&0\\0&{ - 2i}\end{array}} \right]$

b
(b) For $A = \left[ {\begin{array}{*{20}{c}}i&0\\0&{i/2}\end{array}} \right]$,

$adj\,(A) = \left[ {\begin{array}{*{20}{c}}{i/2}&0\\0&i\end{array}} \right]$ and $|A| = - \frac{1}{2}$.

$\therefore $ ${A^{ - 1}} = \frac{1}{\Delta }(adj\,A) = \frac{1}{{ - 1/2}}\,\left[ {\begin{array}{*{20}{c}}{i/2}&0\\0&i\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}{ - i}&0\\0&{ - 2i}\end{array}} \right]$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If $P, Q, R, S$ are represented by the complex numbers $4 + i,\,\,1 + 6i,\,\, - 4 + 3i,\,\, - 1 - 2i$ respectively, then $PQRS$ is a

A particle is moving in a straight line. Its displacement at time $t$ is given by $s = - 4{t^2} + 2t$, then its velocity and acceleration at time $t = {1 \over 2}$ second are

$\int_{}^{} {\frac{1}{{{x^2}}}{{(2x + 1)}^3}} dx = $

The coefficient of ${x^5}$ in the expansion of ${(x + 3)^6}$ is

Let function $F$ be defined as $f\left( x \right) = \int\limits_1^x {\frac{{{e^t}}}{t}dt\,,\,x > 0} $ then the value of the integral $\int\limits_1^x {\frac{{{e^t}}}{{t + a}}dt\,} $ , where $a > 0$ , is

The ${20^{th}}$ term of the series $2 \times 4 + 4 \times 6 + 6 \times 8 + .......$ will be

If $\omega $ is a complex cube root of unity, then for positive integral value of$n$, the product of $\omega .{\omega ^2}.{\omega ^3}........{\omega ^n}$, will be

If the standard deviation of the numbers $-1, 0, 1, k$ is $\sqrt 5$ where $k > 0,$ then $k$ is equal to

In $\Delta ABC ,$ the lengths of sides $AC$ and $AB$ are $12\, cm$ and $5 \,cm ,$ respectively. If the area of $\triangle ABC$ is $30\, cm ^{2}$ and $R$ and $r$ are respectively the radii of circumcircle and incircle of $\Delta ABC$ then the value of $2 R + r ( in cm )$ is equal to ....... .

The number of integral terms in the expansion of $(7^{1/3} + 11^{1/9})^{6561}$ is :-