Question
For any $2-$ rowed square matrix $A,$ if $A \cdot(\operatorname{adj} A)=\left[\begin{array}{ll}8 & 0 \\ 0 & 8\end{array}\right]$ then the value of $| A |$ is

Answer

$(a) \ 8$
$(\operatorname{adj} A)=\left(\begin{array}{ll} 8 & 0 \\ 0 & 8 \end{array}\right) $
$ =8\left(\begin{array}{ll} 1 & 0 \\0 & 1\end{array}\right) $
$=|A| I $
$|A|=8$

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

Similar questions

A person travels 12km in the southward direction and then travels 5km to the right and then travels 15km toward the right and finally travels 5km towards the east, how far is he from his starting place?
  1. 5.5kms
  2. 3km
  3. 13km
  4. 6.4km
If the function $f(x) = x^3 - 9kx^2 + 27x + 30$ is increasing on $R,$ then:
Choose the correct answer from the given four options.
If A and B are two events and $\text{A}\neq\phi,\text{B}\neq\phi,$ then:
If A and B are two events such that $\text{A}\neq\phi,\text{B}=\phi,$ then,
  1. $\text{P}\Big(\frac{\text{A}}{\text{B}}\Big)=\frac{\text{P}(\text{A}\cap\text{B})}{\text{P(B)}}$
  2. $\text{P}\Big(\frac{\text{A}}{\text{B}}\Big)=\text{P(A)}\text{ P(B)}$
  3. $\text{P}\Big(\frac{\text{A}}{\text{B}}\Big)=\text{P}\Big(\frac{\text{B}}{\text{A}}\Big)=1$
  4. $\text{P}\Big(\frac{\text{A}}{\text{B}}\Big)=\frac{\text{P(A)}}{\text{P(B)}}$
The value of $\big[\vec{\text{a}}-\vec{\text{b}},\vec{\text{b}}-\vec{\text{c}},\vec{\text{c}}-\vec{\text{a}}\big],$ where $\big|\vec{\text{a}}\big|=1,\big|\vec{\text{b}}\big|=5,\big|\vec{\text{c}}\big|=3,$ is:
  1. 0
  2. 1
  3. 6
  4. None of these.
The equation of the plane through the origin and parallel to the plane 3x - 4y + 5z + 6 = 0:
  1. 3x - 4y - 5z - 6 = 0
  2. 3x - 4y + 5z + 6 = 0
  3. 3x - 4y + 5z = 0
  4. 3x + 4y - 5z + 6 = 0
The probabilities of a student getting I, II and III division in an examination are $\frac{1}{10},\frac{3}{5}$ and $\frac{1}{4}$ respectively. The probability that the student fails in the examination is.
  1. $\frac{197}{200}$
  2. $\frac{27}{100}$
  3. $\frac{83}{100}$
  4. None of these.
A linear programming of linear functions deals with:
$\int\frac{\text{dx}}{\sqrt{\text{x}}}=$
  1. $\sqrt{\text{x}}+\text{k}$
  2. $2\sqrt{\text{x}}+\text{k}$
  3. $\text{x}+\text{k}$
  4. $\frac{2}{3}\times\frac{3}{2}+\text{k}$
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:
  1. a = 0
  2. b = 0
  3. c = 0
  4. None of these.