Download App

Determinants — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDeterminants1 Mark
MCQ
For an invertible matrix $A$ if $A(\operatorname{adj} A)$ $=\left[\begin{array}{cc}10 & 0 \\ 0 & 10\end{array}\right]$, then $|A|$ is
  • A
    100
  • B
    -100
  • ✓
    10
  • D
    -10
✓

Answer

Correct option: C.
10
(c) : We have, $A(\operatorname{adj} A)=\left[\begin{array}{cc}10 & 0 \\ 0 & 10\end{array}\right]=10\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]=10 I$
We know that $A(\operatorname{adj} A)=|A| I \Rightarrow|A|=10$

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 Determinants→Determinants — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The vectors $a, b$ and $c$ are of the same length and taken pairwise, they form equal angles. If $a = i + j$ and $b = j + k,$ then the co-ordinates of $c$ are
→
If $\vec{\text{a}},\vec{\text{b}}$ represent the diagonals of a rhombus, then:
  1. $\vec{\text{a}}\times\vec{\text{b}}=\vec{0}$
  2. $\vec{\text{a}}.\vec{\text{b}}=0$
  3. $\vec{\text{a}}.\vec{\text{b}}=1$
  4. $\vec{\text{a}}\times\vec{\text{b}}=\vec{\text{a}}$
→
$\int_{}^{} {\frac{{dx}}{{(1 + {x^2})\sqrt {1 - {x^2}} }} = } $
→
The unit vector perpendicular to the vectors $6i + 2j + 3k$ and $3i - 6j - 2k,$ is
→
If the function $f(x) = \left\{ \begin{array}{l}\frac{{k\cos x}}{{\pi - 2x}},{\rm{when }}x \ne \frac{\pi }{2}\\3,\;\;\;\;\;\;\;\;\;{\rm{when }}x = \frac{\pi }{2}\end{array} \right.$ be continuous at $x = \frac{\pi }{2}$, then $ k =$ 
→
If $\text{y}=\log\Big(\frac{1-\text{x}^2}{1+\text{x}^2}\Big),$ then $\frac{\text{dy}}{\text{dx}}=$
  1. $\frac{4\text{x}^3}{1-\text{x}^4}$
  2. $-\frac{4\text{x}}{1-\text{x}^4}$
  3. $\frac{1}{4-\text{x}^4}$
  4. $-\frac{4\text{x}^3}{1-\text{x}^4}$
→
$\int\limits_0^\pi  {} $ $(x · sin^2x · cos x) dx $ =
→
The maximum value of  $xy $ when $x + 2y = 8$ is
→
Number of solutions of the equation $2tan^{-1}(cos^2x) = tan^{-1}(2cosec^2x)$ in $\left[ {0,5\pi } \right]$ is $m$ , then
→
A bag X contains 2 white and 3 black balls and another bag Y contains 4 white and 2 black balls. One bag is selected at random and a ball is drawn from it. Then, the probability chosen to be white is,
→