If A = [ * 20 c 2&2 &b ] and A^2 = O, then (a,b) = - Vidyadip

MCQ

If $A = \left[ {\begin{array}{*{20}{c}}2&2\\a&b\end{array}} \right]$ and ${A^2} = O$, then $(a,b) = $

✓
$( - 2,\, - 2)$
B
$(2,\, - 2)$
C
$( - 2,\,2)$
D
$(2,\,2)$

✓

Answer

Correct option: A.

$( - 2,\, - 2)$

a
(a) ${A^2} = \left[ {\begin{array}{*{20}{c}}2&2\\a&b\end{array}} \right]\,\left[ {\begin{array}{*{20}{c}}2&2\\a&b\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}{4 + 2a}&{4 + 2b}\\{2a + ab}&{2a + {b^2}}\end{array}} \right] = 0 = \left[ {\begin{array}{*{20}{c}}0&0\\0&0\end{array}} \right]$

$ \Rightarrow \,\,4 + 2a = 0,4 + 2b = 0,$$2a + ab = 0,$

$2a + {b^2} = 0$ must be consistent.

$ \Rightarrow $ $a = - 2$, $b = - 2$.

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

The value of the definite integral $\int\limits_0^{\pi /2} {\sqrt {\tan \,x\,} } dx$, is

If $\int\frac{\cos8\text{x}+1}{\tan2\text{x}-\cot2\text{x}}\text{ dx}=\text{a}\cos8\text{x}+\text{C},$ then a =

Let $\vec{p}=2 \hat{i}+\hat{j}+3 \hat{k}$ and $\vec{q}=\hat{i}-\hat{j}+\hat{k}$. If for some real numbers $\alpha, \beta$ and $\gamma$, we have $15 \hat{i}+10 \hat{j}+6 \hat{k}=\alpha(2 \vec{p}+\vec{q})+\beta(\vec{p}-2 \vec{q})+\gamma(\vec{p} \times \vec{q})$, then the value of $\gamma$ is. . . . .

A bag contains 5 red and 3 blue balls. If 3 balls are drawn at random without replacement, then the probability that exactly two of the three balls were red, the first ball being red, is

The maximum number of equivalence relations on the set $A=\{1,2,3\}$ are

The number of solutions of the equations $x + 4y - z = 0,$ $3x - 4y - z = 0,\,x - 3y + z = 0$ is

The corner points of the feasible region determined by the following system of linear inequalities:
$2 x+y \leq 10, x+3 y \leq 15, x, y \geq 0$ are $(0,0),(5,0),(3,4)$ and $(0,5)$. Let $Z=p x+q y$, where $p, q \geq 0$.
Condition on $p$ and $q$ so that the maximum of $Z$ occurs at both $(3, 4)$ and $(0, 5)$ is

The point on the curve $y^2 = x$ where tangent makes $45^\circ $ angle with $x-$ axis is :

The number of distinct real roots of $\begin{vmatrix}\text{cosec}&\sec\text{x}&\sec\text{x}\\\sec\text{x}&\text{cosec}\text{x}&\sec\text{x}\\\sec\text{x}&\sec\text{x}&\text{cosecx}\end{vmatrix}=0$ lies in the interval $-\frac{\pi}{4}\leq\text{x}\leq\frac{\pi}{4}$ is:

The direction cosines of the normal to the plane $x + 2y - 3z + 4 = 0$ are