Download App

STD 12 - 3 and 4 . determinant and metrices — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 3 and 4 . determinant and metrices1 Mark
MCQ
The matrix $A = \left[ {\begin{array}{*{20}{c}}{1/\sqrt 2 }&{1/\sqrt 2 }\\{ - 1/\sqrt 2 }&{ - 1/\sqrt 2 }\end{array}} \right]$ is
  • A
    Unitary
  • B
    Orthogonal
  • ✓
    Nilpotent
  • D
    Involutory
✓

Answer

Correct option: C.
Nilpotent
c
(c) ${A^2} = A\,.\,A = \left[ {\begin{array}{*{20}{c}}{1/\sqrt 2 }&{1/\sqrt 2 }\\{ - 1/\sqrt 2 }&{ - 1/\sqrt 2 }\end{array}} \right]\,\left[ {\begin{array}{*{20}{c}}{1/\sqrt 2 }&{1/\sqrt 2 }\\{ - 1/\sqrt 2 }&{ - 1/\sqrt 2 }\end{array}} \right]$

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

$\therefore $ Matrix $A$ is nilpotent of order  $2$ .

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

$\int\limits^{\frac{\pi}{2}}_0\sin2\text{x }\log\tan\text{x dx}$ is equal to:
→
Choose the correct answer in the following. Area bounded by the curve $y = x^3,$ the $x-$ axis and the ordinates $x = –2$ and $x = 1$ is :
→
Choose the correct answer from the given four options.The curve for which the slope of the tangent at any point is equal to the ratio of the abcissa to the ordinate of the point is :
→
The general solution of the differential equation $\frac{\text{dy}}{\text{dx}}+\text{y}\ \text{g}(\text{x})=\text{g}(\text{x})\ \text{g}'(\text{x})$ is a given function of x, is:
→
If $y = {\left[ {x + \sqrt {{x^2} - 1} } \right]^{15}} + {\left[ {x - \sqrt {{x^2} - 1} } \right]^{15}}$ , then $\left( {{x^2} - 1} \right)\frac{{{d^2}y}}{{d{x^2}}} + x\frac{{dy}}{{dx}}$ is equal to
→
A box contains $b$ blue balls and $r$ red balls. A ball is drawn randomly from the box and is returned to the box with another ball of the same colour. The probability that the second ball drawn from the box is blue, is
→
Let L denote the set of all straight lines in a plane. Let a relation R be defined by lRm if l is perpendicular to m for all l, m ∈ L. Then, R is:
→
The function $f(x) = x + \sin x$ has
→
The value of $\int_0^1 {(1 + {e^{ - {x^2}}})} \,dx = $
→
$\int_{}^{} {\frac{{{x^4} + {x^2} + 1}}{{{x^2} - x + 1}}\;dx = } $
→