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

More "M.C.Q (1 Marks)" from STD 12 - 3 and 4 . determinant and metrices→STD 12 - 3 and 4 . determinant and metrices — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

If ${\sec ^{ - 1}}x = {\rm{cose}}{{\rm{c}}^{ - 1}}y,$ then ${\cos ^{ - 1}}\frac{1}{x} + {\cos ^{ - 1}}\frac{1}{y} = $

The determinant $\begin{vmatrix}\text{b}^2-\text{ab}&\text{b}-\text{c}&\text{bc}-\text{ac}\\\text{ab}-\text{a}^2&\text{a}-\text{b}&\text{b}^2-\text{ab}\\\text{bc}-\text{ac}&\text{c}-\text{a}&\text{ab}-\text{a}^2\end{vmatrix}$ equals :

If $\frac{\text{dy}}{\text{dx}}=\text{x}^{-3}$ then $y:$

Let the area of the region enclosed by the curves $y=3 x, 2 y=27-3 x$ and $y=3 x-x \sqrt{x}$ be $A$. Then $10 \mathrm{~A}$ is equal to

If $\left(\frac{1}{2}, \frac{1}{3}, n\right)$ are the direction cosines of a line, then the value of $n$ is

Which of the termis not used in a linear programming problem:

If the projection of the vector $\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}}$ on the sum of the two vectors $2 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}-5 \hat{\mathrm{k}}$ and $-\lambda \hat{i}+2 \hat{j}+3 \hat{k}$ is $1,$ then $\lambda$ is equal to ..... .

If the multiplicative group of $2 × 2$ matrices of the form $\left( {\begin{array}{*{20}{c}}a&a\\a&a\end{array}} \right)$, for $a \ne 0$ and $a \in R$, then the inverse of $\left( {\begin{array}{*{20}{c}}2&2\\2&2\end{array}} \right)$ is

Family $y = Ax + {A^3}$ of curve represented by the differential equation of degree

Choose the correct answer from the given four options. Suppose a random variable $X$ follows the binomial distribution with parameters $n$ and $p,$ where $0 < p < 1.$ If $\frac{\text{P}(\text{x}=\text{r})}{\text{P}(\text{x}=\text{n}–\text{r})}$ is independent of $n$ and $r,$ then $p$ equals :