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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If the odds in favour of an event be $3 : 5$, then the probability of non-occurrence of the event is

If the function $f(x) = - 4{e^{\left( {\frac{{1 - x}}{2}} \right)}} + 1 + x + \frac{{{x^2}}}{2} + \frac{{{x^3}}}{3}$ and $g(x)=f^{-1}(x) \,;$ then the value of $g'(-\frac{7}{6})$ equals

$2{\tan ^{ - 1}}(\cos x) = {\tan ^{ - 1}}({\rm{cose}}{{\rm{c}}^2}x),$ then $ x =$

The points $( - a, - b),\;(a,b),\;({a^2},ab)$are

If the coefficient of ${(2r + 4)^{th}}$ and ${(r - 2)^{th}}$ terms in the expansion of ${(1 + x)^{18}}$ are equal, then$ r=$

The locus of the mid point of the focal radii of a variable point moving on the parabola, $y^2 = 4ax$ is a parabola whose

$\int_{ - a}^a {\sin x\,f(\cos x)\,dx = } $

The area of the quadrilateral formed by the tangents at the end points of latus rectum to the ellipse $\frac{{{x^2}}}{9} + \frac{{{y^2}}}{5} = 1$, is .............. $\mathrm{sq. \,units}$

The second order differential equation is

The conjugate of the complex number $\frac{{2 + 5i}}{{4 - 3i}}$ is