Which of the following is a nilpotent matrix - Vidyadip

MCQ

Which of the following is a nilpotent matrix

A
$\left[ {\begin{array}{*{20}{c}}1&0\\0&1\end{array}} \right]$
B
$\left[ {\begin{array}{*{20}{c}}{\cos \theta }&{ - \sin \theta }\\{\sin \theta }&{\cos \theta }\end{array}} \right]$
✓
$\left[ {\begin{array}{*{20}{c}}0&0\\1&0\end{array}} \right]$
D
$\left[ {\begin{array}{*{20}{c}}1&1\\1&1\end{array}} \right]$

✓

Answer

Correct option: C.

$\left[ {\begin{array}{*{20}{c}}0&0\\1&0\end{array}} \right]$

c
$A$ is nilpotent if $A^m = 0$ and $A^{m-1} \neq 0$

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 3 and 4 . determinant and metrices→3 and 4 . determinant and metrices — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The left-hand derivative of $f(x) = [x]\sin (\pi x)$ at $x = k,\,\,k $ is an integer and $[x]$= greatest integer $ \le x,\,$ is

Suppose $A$ is $3 \times 3$ matrix consisting of integer entries that are chosen at random from the set $\{-1000,-999, \ldots 999,1000\}$. Let $P$ be the probability that either $A^2=-I$ or $A$ is diagonal, where $I$ is the $3 \times 3$ identity matrix. Then,

The equation of the normal to the curve 3x² - y² = 8 which is parallel to x + 3y = 8 is:

x + 3y = 8
x + 3y + 8 = 0
x + 3y ± 8 = 0
x + 3y = 0

$\int_0^{\frac{\pi}{6}} \sec ^2\left(x-\frac{\pi}{6}\right) d x$ is equal to :

Let $f(x) = e^x -x$ and $g(x) = x^2 -x$, $\forall \in R$. Then the set of all $x \in R$, where the function $h(x) = (fog)\, (x)$ is increasing is

A box contains $15$ green and $10$ yellow balls. lf $10$ balls are randomly drawn, one-by-one, with replacement, then the variance of the number of green balls drawn is :

If $y=\tan ^{-1}\left(e^{2 x}\right)$, then $\frac{d y}{d x}$ is equal to

Find the area of the triangle whose vertices are $(3,8),(-4,2)$ and $(5,1)$

The graph of the inequality $2 x+3 y>6$ is

Match List $I$ with List $II$ and select the correct answer using the code given below the lists :

List $I$	List $II$
$P.\quad$ Volume of parallelopiped determined by vectors $\vec{a}, \vec{b}$ and $\overrightarrow{ c }$ is $2$ . Then the volume of the parallelepiped determined by vectors $2(\vec{a} \times \vec{b}), 3(\vec{b} \times \vec{c})$ and $(\vec{c} \times \vec{a})$ is	$1.\quad$ $100$
$Q.\quad$ Volume of parallelepiped determined by vectors $\vec{a}, \vec{b}$ and $\vec{c}$ is $5$ . Then the volume of the parallelepiped determined by vectors $3(\overrightarrow{ a }+\overrightarrow{ b }),(\overrightarrow{ b }+\overrightarrow{ c })$ and $2(\overrightarrow{ c }+\overrightarrow{ a })$ is	$2.\quad$ $30$
$R.\quad$ Area of a triangle with adjacent sides determined by vectors $\vec{a}$ and $\vec{b}$ is $20$ . Then the area of the triangle with adjacent sides determined by vectors $(2 \vec{a}+3 \vec{b})$ and $(\vec{a}-\vec{b})$ is	$3.\quad$ $24$
$S.\quad$ Area of a paralelogram with adjacent sides determined by vectors $\vec{a}$ and $\vec{b}$ is $30$ . Then the area of the parallelogram with adjacent sides determined by vectors $(\vec{a}+\vec{b})$ and $\vec{a}$ is	$4.\quad$ $60$

Codes: $ \quad P \quad Q \quad R \quad S $