If A= [ ll 0 & 2 2 & 0 ], then A^2 is equal to - Vidyadip

MCQ

If $A=\left[\begin{array}{ll}0 & 2 \\ 2 & 0\end{array}\right]$, then $A^2$ is equal to

A
$\left[\begin{array}{ll}0 & 2 \\ 2 & 0\end{array}\right]$
B
$\left[\begin{array}{ll}4 & 0 \\ 4 & 0\end{array}\right]$
C
$\left[\begin{array}{ll}0 & 2 \\ 0 & 4\end{array}\right]$
✓
$\left[\begin{array}{ll}4 & 0 \\ 0 & 4\end{array}\right]$

✓

Answer

Correct option: D.

$\left[\begin{array}{ll}4 & 0 \\ 0 & 4\end{array}\right]$

(d) : We have, $A=\left[\begin{array}{ll}0 & 2 \\ 2 & 0\end{array}\right]$
$
\Rightarrow \quad A^2=\left[\begin{array}{ll}
0 & 2 \\
2 & 0
\end{array}\right]\left[\begin{array}{ll}
0 & 2 \\
2 & 0
\end{array}\right]=\left[\begin{array}{ll}
0+4 & 0+0 \\
0+0 & 4+0
\end{array}\right]=\left[\begin{array}{ll}
4 & 0 \\
0 & 4
\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 Matrices→Matrices — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

$\int \limits_{\pi / 6}^{\pi / 3} \tan ^{3} x \cdot \sin ^{2} 3 x\left(2 \sec ^{2} x \cdot \sin ^{2} 3 x+3 \tan x \cdot \sin 6 x\right) d x$ is equal to

$\tan^{-1}(\sqrt{3})$

There are three bags $B_1, B_2$ and $B_3$. The bag $B_1$ contains $5$ red and $5$ green balls, $B_2$ contains $3$ red and 5 green balls, and $B_3$ contains $5$ red and $3$ green balls, Bags $B_1, B_2$ and $B_3$ have probabilities $\frac{3}{10}, \frac{3}{10}$ and $\frac{4}{10}$ respectively of being chosen. A bag is selected at random and a ball is chosen at random from the bag. Then which of the following options is/are correct?

$(1)$ Probability that the selected bag is $B _3$ and the chosen ball is green equals $\frac{3}{10}$

$(2)$ Probability that the chosen ball is green equals $\frac{39}{80}$

$(3)$ Probability that the chosen ball is green, given that the selected bag is $B_3$, equals $\frac{3}{8}$

$(4)$ Probability that the selected bag is $B_3$, given that the chosen balls is green, equals $\frac{5}{13}$

The matrix $\left[ {\begin{array}{*{20}{c}}0&5&{ - 7}\\{ - 5}&0&{11}\\7&{ - 11}&0\end{array}} \right]$is known as

The system of linear equations:
x + y + z = 2
2x + y − z = 3
3x + 2y + kz = 4
has a unique solution if

The existence of the unique solution of the system of equations:
$x+y+z=\lambda$
$5 x-y+\mu z=10$
$2 x+3 y-z=6 $ depends on

The function $f(x) = {(x - 3)^2}$ satisfies all the conditions of mean value theorem in $[3, 4].$ A point on $y = {(x - 3)^2}$, where the tangent is parallel to the chord joining $ (3, 0)$ and $(4, 1)$ is

The distance of the point $Q(0,2,-2)$ form the line passing through the point $\mathrm{P}(5,-4,3)$ and perpendicular to the lines $\overrightarrow{\mathrm{r}}=(-3 \hat{\mathrm{i}}+2 \hat{\mathrm{k}})$ $\lambda(2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+5 \hat{\mathrm{k}}), \quad \lambda \in \mathbb{R} \quad$ and $\quad \overrightarrow{\mathrm{r}}=(\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+\hat{\mathrm{k}})+$ $\mu(-\hat{i}+3 \hat{J}+2 \hat{K}), \mu \in \mathbb{R}$ is

The area enclosed by the curves $y = x^2, y = x^3 , x = 0$ and $x = p,$ where $p > 1$ , is $1/6$. The $p$ equals

Area of the region bounded by the curve $y=e^x$ and lines $x=0$ and $y=e$ is

$(A)$ $e-1$ $(B)$ $\int_1^e \ln (e+1-y) d y$ $(C)$ $e-\int_0^1 e^x d x$ $(D)$ $\int_1^r \ln y d y$