If A is a singular matrix, then A (adj A) is a. - Vidyadip

MCQ

If $A$ is a singular matrix, then $A \text{(adj A)}$ is a.

A
scalar matrix
✓
zero matrix
C
identity matrix
D
orthogonal matrix

✓

Answer

Correct option: B.

zero matrix

Given $A$ is a singular matrix.
$\Rightarrow ∣A∣ = 0$
$A(\text{adj A}) = |A| I = 0I = O$
$\therefore \text{A(adj A)}$ is a zero matrix.

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

If ${e^{f(x)}} = \frac{{10 + x}}{{10 - x}},\;x \in ( - 10,\;10)$ and $f(x) = kf\left( {\frac{{200x}}{{100 + {x^2}}}} \right)$, then $k = $

The value of $\int\frac{\sin\text{x}+\cos\text{x}}{\sqrt{1-\sin2\text{x}}}\text{ dx}$ is equal to:

$\int_0^{\pi /6} {(2 + 3{x^2})\cos 3x\,dx = } $

If $\alpha \neq \mathrm{a}, \beta \neq \mathrm{b}, \gamma \neq \mathrm{c}$ and $\left|\begin{array}{lll}\alpha & \mathrm{b} & \mathrm{c} \\ \mathrm{a} & \beta & \mathrm{c} \\ \mathrm{a} & \mathrm{b} & \gamma\end{array}\right|=0$,then $\frac{a}{\alpha-a}+\frac{b}{\beta-b}+\frac{\gamma}{\gamma-c}$ is equal to :

Which of the following is not correct?

For the $LP$ problem

"Maximize $z=x+4 y$

subject to $3 x+6 y \leq 6,4 x+8 y \geq 16$ and $x \geq 0, y \geq 0$."

Let $\vec p,\,\vec q$ and $\vec r$ be three non coplanar unit vectors equally inclined to each other at an acute angle $\theta $ . The value of $\left| {\vec p \times \left( {\vec q \times \vec r} \right)} \right|$ is

The value of $\int {\frac{{\log x}}{{{{(x + 1)}^2}}}dx} $ is

If $\text{A}=\begin{bmatrix} 1 & 0 & 1 \\ 0 & 0 & 1 \\ \text{a} & \text{b} & 2 \end{bmatrix},$ then $aI + bA + 2 A^2$ equals:

Choose the correct answer in each of the following:
The mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on one face is