Q. If $A=\begin{bmatrix}1 & -1 & 2 \\ 2 & 3 & 1 \\ 1 & -2 & 3\end{bmatrix}$ then $\text{adj}\left(A^{-1}\right)=$

KCETKCET 2022 Report Error

A

$\frac{1}{2} A$

B

$2 A$

C

$8 A$

D

$\frac{1}{8} A$

Solution:

$\text{adj}\left(A^{-1}\right)=(\text{adj} A)^{-1}=\frac{A}{|A|}$ Now,
$|A|=1 .(9+2)+1 \cdot(6-1)+2 \cdot(-4-3)$
$=11+5-14=2$
$\therefore(\text{adj} A)^{-1}=\frac{1}{2} A$

Questions from KCET 2022

1. It is observed that $23 x+17 y=1$ for some integers $x$ and $y$ . Then $(x, y)=$

2. The sum of all the positive divisors of $180$ excluding $1$ and itself is

3. If $x+y+z=\pi$ then the value of $\begin{vmatrix}\sin (x+y+z) & \sin B & \cos z \\ -\sin B & 0 & \tan A \\ \cos (x+y) & -\tan A & 0\end{vmatrix}$ is

4. If the value of a third order determinant is $11$ , then the value of the determinant formed by the cofactors will be

5. If $A=\begin{bmatrix}1 & -1 & 2 \\ 2 & 3 & 1 \\ 1 & -2 & 3\end{bmatrix}$ then $\text{adj}\left(A^{-1}\right)=$

Mathematics Most Viewed Questions

1. The solution of $\frac{dy}{dx} = \frac{y}{x}+\tan \frac{y}{x}$ is

WBJEE 2011 Differential Equations

2. The solution of the differential equation $\frac{dy}{dx} = (x +y)^2$ is

COMEDK 2009 Differential Equations

3. $\int\frac{1}{\sin x\, \cos x}$ dx is equal to

KEAM 2016 Integrals

4. If $\begin{bmatrix}1&- \tan\theta \\ \tan \theta&1\end{bmatrix}\begin{bmatrix}1&\tan \theta \\ - \tan \theta &1\end{bmatrix}^{-1} = \begin{bmatrix}a&-b\\ b&a\end{bmatrix}$ then

COMEDK 2009 Matrices

5. The value of $\int{\frac{{{x}^{2}}+1}{{{x}^{4}}-{{x}^{2}}+1}}dx$ is

KEAM 2007 Integrals

Q. If A=[1−122311−23]A=\begin{bmatrix}1 & -1 & 2 \\ 2 & 3 & 1 \\ 1 & -2 & 3\end{bmatrix} then adj(A−1)=\text{adj}\left(A^{-1}\right)=

12A\frac{1}{2} A

2A2 A

8A8 A

18A\frac{1}{8} A

adj(A−1)=(adjA)−1=A|A|\text{adj}\left(A^{-1}\right)=(\text{adj} A)^{-1}=\frac{A}{|A|} Now, |A|=1.(9+2)+1⋅(6−1)+2⋅(−4−3)|A|=1 .(9+2)+1 \cdot(6-1)+2 \cdot(-4-3) =11+5−14=2=11+5-14=2 \therefore(\text{adj} A)^{-1}=\frac{1}{2} A\therefore(\text{adj} A)^{-1}=\frac{1}{2} A

Questions from KCET 2022

1. It is observed that 23 x+17 y=123 x+17 y=1 for some integers xx and yy. Then (x, y)=(x, y)=

2. The sum of all the positive divisors of 180180 excluding 11 and itself is

3. If x+y+z=\pix+y+z=\pi then the value of \begin{vmatrix}\sin (x+y+z) & \sin B & \cos z \\ -\sin B & 0 & \tan A \\ \cos (x+y) & -\tan A & 0\end{vmatrix}\begin{vmatrix}\sin (x+y+z) & \sin B & \cos z \\ -\sin B & 0 & \tan A \\ \cos (x+y) & -\tan A & 0\end{vmatrix} is

4. If the value of a third order determinant is 11 11 , then the value of the determinant formed by the cofactors will be

5. If A=\begin{bmatrix}1 & -1 & 2 \\ 2 & 3 & 1 \\ 1 & -2 & 3\end{bmatrix}A=\begin{bmatrix}1 & -1 & 2 \\ 2 & 3 & 1 \\ 1 & -2 & 3\end{bmatrix} then \text{adj}\left(A^{-1}\right)=\text{adj}\left(A^{-1}\right)=

Mathematics Most Viewed Questions

1. The solution of \frac{dy}{dx} = \frac{y}{x}+\tan \frac{y}{x}\frac{dy}{dx} = \frac{y}{x}+\tan \frac{y}{x} is

2. The solution of the differential equation \frac{dy}{dx} = (x +y)^2\frac{dy}{dx} = (x +y)^2 is

3. \int\frac{1}{\sin x\, \cos x}\int\frac{1}{\sin x\, \cos x} dx is equal to

5. The value of \int{\frac{{{x}^{2}}+1}{{{x}^{4}}-{{x}^{2}}+1}}dx \int{\frac{{{x}^{2}}+1}{{{x}^{4}}-{{x}^{2}}+1}}dx is

Latest Updates

Q. If $A=\begin{bmatrix}1 & -1 & 2 \\ 2 & 3 & 1 \\ 1 & -2 & 3\end{bmatrix}$ then $\text{adj}\left(A^{-1}\right)=$

$\frac{1}{2} A$

$2 A$

$8 A$

$\frac{1}{8} A$

$\text{adj}\left(A^{-1}\right)=(\text{adj} A)^{-1}=\frac{A}{|A|}$ Now,
$|A|=1 .(9+2)+1 \cdot(6-1)+2 \cdot(-4-3)$
$=11+5-14=2$
$\therefore(\text{adj} A)^{-1}=\frac{1}{2} A$

1. It is observed that $23 x+17 y=1$ for some integers $x$ and $y$ . Then $(x, y)=$

2. The sum of all the positive divisors of $180$ excluding $1$ and itself is

3. If $x+y+z=\pi$ then the value of $\begin{vmatrix}\sin (x+y+z) & \sin B & \cos z \\ -\sin B & 0 & \tan A \\ \cos (x+y) & -\tan A & 0\end{vmatrix}$ is

4. If the value of a third order determinant is $11$ , then the value of the determinant formed by the cofactors will be

5. If $A=\begin{bmatrix}1 & -1 & 2 \\ 2 & 3 & 1 \\ 1 & -2 & 3\end{bmatrix}$ then $\text{adj}\left(A^{-1}\right)=$

1. The solution of $\frac{dy}{dx} = \frac{y}{x}+\tan \frac{y}{x}$ is

2. The solution of the differential equation $\frac{dy}{dx} = (x +y)^2$ is

3. $\int\frac{1}{\sin x\, \cos x}$ dx is equal to

5. The value of $\int{\frac{{{x}^{2}}+1}{{{x}^{4}}-{{x}^{2}}+1}}dx$ is