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

MCQ

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

A
$\alpha = {a^2} + {b^2},\beta = ab$
✓
$\alpha = {a^2} + {b^2},\beta = 2ab$
C
$\alpha = {a^2} + {b^2},\beta = {a^2} - {b^2}$
D
$\alpha = 2ab,\beta = {a^2} + {b^2}$

✓

Answer

Correct option: B.

$\alpha = {a^2} + {b^2},\beta = 2ab$

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

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

If $\vec{a}, \vec{b}$ and $(\vec{a}+\vec{b})$ are all unit vectors and $\theta$ is the angle between $\vec{a}$ and $\vec{b}$, then the value of $\theta$ is :

The order and degree of the differential equation $\rho = \frac{{{{\left[ {1 + {{\left( {\frac{{dy}}{{dx}}} \right)}^2}} \right]}^{3/2}}}}{{{d^2}y/d{x^2}}}$ are respectively

The function, $f (x) = [|x|] -|[x]|$ where $[ x ]$ denotes greatest integer function

Let $a_n=\int_{-\pi}^\pi|x-1| \cos n x d x$ for all natural numbers $n$. Then, the sequence $\left(a_n\right)_{n \geq 0}$ satisfies

Determinant $\left|\begin{array}{cc}1 & \log _b a \\ \log _a b & 1\end{array}\right|=$

Consider the following statements:

$\tan^{-1} 1+ \tan^{-1} (0.5) = \dfrac {\pi}2$
$\sin^{-1}{\cfrac{1}{3} }+ \cos^{-1}{\cfrac{1}{3}} =\cfrac{\pi}{2}$

Which of the above statements is/are correct ?

The area bounded by the curve $y = 4x - x^2$ and the $x-$ axis is:

Choose the correct answer from the given four options. The matrix $\begin{bmatrix}1&0&0\\0&2&0\\0&0&4\end{bmatrix}$ is a:

Area between the parabolas $y^2=4 a x$ and $x^2=4 a y$ is:

If $\text{f(x)}=\begin{cases}\frac{\sin(\text{a}+1)}{\text{x}},&\text{x}<0\\\text{c},&\text{x}=0\\\frac{\sqrt{\text{x+bx}^2}-\sqrt{\text{x}}}{\text{bx}\sqrt{\text{x}}},&\text{x}>0&\end{cases}$ is continuouse at x = 0, then: