Download App

Matrics — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsMatrics2 Marks
MCQ
If A is a square matrix such that $A(\operatorname{adj} A)=\left[\begin{array}{lll}4 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 4\end{array}\right]$, then $\frac{|\operatorname{adj}(\operatorname{adj} A)|}{|\operatorname{adj} A|}$ is equal to
  • A
    256
  • ✓
    16
  • C
    32
  • D
    64
✓

Answer

Correct option: B.
16
(B) A. $(\operatorname{adj} A)=\left[\begin{array}{lll}4 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 4\end{array}\right]$ . . .(i)
$=4\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]$
$=4 . I$
Using Shortcut 4(i),
$A (\operatorname{adj} A )=| A | . I$,
$|A|=4$
From (i), $| A | \cdot|\operatorname{adj} A |=64$
$\Rightarrow|\operatorname{adj} A|=\frac{64}{4}=16$
Using Shortcut 4(xiv),
$|\operatorname{adj}(\operatorname{adj} A )|=| A |^{( n -1)^2}$
$=| A |^{(3-1)^2}$
$=(4)^4=256$
$\therefore \frac{|\operatorname{adj}(\operatorname{adj} A)|}{|\operatorname{adj} A|}=\frac{256}{16}=16$

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 "MCQ" from Matrics→Matrics — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

If $\text{x}=\text{at}^2,\text{y}=2\text{at}$ then $\frac{\text{d}^2\text{y}}{\text{dx}^2}$=
→
$\int_0^{\frac{\pi}{2}} \frac{\sin ^{1000} x d x}{\sin ^{1000} x+\cos ^{1000} x}$ is equal to
→
In a $\triangle A B C$, if $\frac{b+c}{11}=\frac{c+a}{12}=\frac{a+b}{13}$, then $\cos C=$
→
Let $\text{f(x)}=\text{x}+\text{b}|\text{x}|+\text{c}|\text{x}|^4,$ where $a, b,$ and $c$ are real constants. Then, $f (x)$ is differentiable at $x = 0,$ if:
→
The degree of the differential equation $2\text{x}^{2}\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}+3\frac{\text{dy}}{\text{dx}}+\text{y}=0$ is:
→
The distance of the point (3, 4, 5) from Y- axis is
→
The projections of a line segment on $x, y$ and $z$ axes are $12, 4$ and $3$ respectively. The length and direction cosines of the line segment are:
→
The value of integration $\int_{\frac{-\pi}{4}}^{\frac{\pi}{4}}\left(\lambda|\sin x|+\frac{\mu \sin x}{1+\cos x}+\gamma\right) d x$
→
Which of the following equations represents a pair of real and coincident straight lines?
→
Evaluate : $\int_0^{\pi / 2} \frac{\cos x}{\left(\cos \frac{x}{2}+\sin \frac{x}{2}\right)^3} d x$
→