If A = ( * 20 c i&1 0&i ), then A^4 equals - Vidyadip

MCQ

If $A = \left( {\begin{array}{*{20}{c}}i&1\\0&i\end{array}} \right)$, then ${A^4}$ equals

✓
$\left( {\begin{array}{*{20}{c}}1&{ - 4i}\\0&1\end{array}} \right)$
B
$\left( {\begin{array}{*{20}{c}}{ - 1}&{ - 4i}\\0&{ - 1}\end{array}} \right)$
C
$\left( {\begin{array}{*{20}{c}}{ - i}&4\\0&i\end{array}} \right)$
D
$\left( {\begin{array}{*{20}{c}}1&4\\0&1\end{array}} \right)$

✓

Answer

Correct option: A.

$\left( {\begin{array}{*{20}{c}}1&{ - 4i}\\0&1\end{array}} \right)$

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

${A^4} = \left[ {\begin{array}{*{20}{c}}1&{ - 4i}\\0&1\end{array}} \right]$.

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

A unit vector perpendicular to the plane determined by the points $ (1, -1, 2), (2, 0, -1) $ and $ (0, 2, 1) $ is

If for $\theta \in\left[-\frac{\pi}{3}, 0\right]$, the points $(x, y)=\left(3 \tan \left(\theta+\frac{\pi}{3}\right), 2 \tan \left(\theta+\frac{\pi}{6}\right)\right)$ lie on
$x y+\alpha x+\beta y+\gamma=0$, then $\alpha^{2}+\beta^{2}+\gamma^{2}$ is equal to :

Let $M$ be a $3 \times 3$ matrix satisfying $M\left[\begin{array}{l}0 \\ 1 \\ 0\end{array}\right]=\left[\begin{array}{c}-1 \\ 2 \\ 3\end{array}\right], M\left[\begin{array}{c}1 \\ -1 \\ 0\end{array}\right]=\left[\begin{array}{c}1 \\ 1 \\ -1\end{array}\right],$ and $M\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right]=\left[\begin{array}{c}0 \\ 0 \\ 12\end{array}\right]$ Then the sum of the diagonal entries of $M$ is

Let $S_{1}: x^{2}+y^{2}=9$ and $S_{2}:(x-2)^{2}+y^{2}=1$. Then the locus of center of a variable circle $S$ which touches $S_{1}$ internally and $S_{2}$ externally always passes through the points :

If $a$ and $c$ are positive real numbers and the ellipse $\frac{{{x^2}}}{{4{c^2}}} + \frac{{{y^2}}}{{{c^2}}} = 1$ has four distinct points in common with the circle $x^2 + y^2 = 9a^2$ , then

The sum of squares of all possible values of $k$, for which area of the region bounded by the parabolas $2 \mathrm{y}^2=\mathrm{kx}$ and $\mathrm{ky}^2=2(\mathrm{y}-\mathrm{x})$ is maximum, is equal to :

If $y=y(x)$ is the solution curve of the differential equation $\frac{d y}{d x}+y \tan x=x \sec x, \quad 0 \leq x \leq \frac{\pi}{3}$, $y (0)=1$, then $y \left(\frac{\pi}{6}\right)$ is equal to

If ${a_{ij}} = \frac{1}{2}(3i - 2j)$ and $A = {[{a_{ij}}]_{2 \times 2}}$, then $A$ is equal to

The following points $A\, (2a,\, 4a),\, B(2a,\, 6a)$ and $C$ $(2a + \sqrt 3 a,\,5a)$, $(a > 0)$ are the vertices of

The value of $k$ for which one of the roots of ${x^2} - x + 3k = 0$ is double of one of the roots of ${x^2} - x + k = 0$ is