If A is a non-singular square matrix such that |A| = 10, find |A-… - Vidyadip

Question

If A is a non-singular square matrix such that |A| = 10, find |A^-1|.

✓

Answer

$\big|\text{A}^{-1}\big|=\Big|\frac{1}{\text{A}}\Big|$

$=\Big|\frac{1}{\text{A}}\Big|$

$=\frac{1}{10}\ \big[\because|\text{A}|=10\text{ (Given})\big]$

Hence, $\big|\text{A}^{-1}\big|=\frac{1}{10}$

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 "2 Marks" from Adjoint and Inverse of a Matrix→Adjoint and Inverse of a Matrix — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Let A = {x ∈ R : -4 ≤ x ≤ 4 and x ≠ 0} and f : A → R be defined by $\text{f(x)}=\frac{|\text{x}|}{\text{x}}.$ Write the range of f.

Find the value of the determinant $\begin{vmatrix}2^2&2^3&2^4\\2^3&2^4&2^5\\2^4&2^5&2^6\end{vmatrix}$

If $x\left[\begin{array}{l}2 \\ 3\end{array}\right]+y\left[\begin{array}{c}-1 \\ 1\end{array}\right]=\left[\begin{array}{c}10 \\ 5\end{array}\right]$, find the values of $\mathrm{x}$ and $\mathrm{y}$.

Determine the order and degree of the following differential equations. state also whether they are linear or non linear.
$\frac{\text{d}^4\text{y}}{\text{dx}^4}=\Big\{\text{c}+\Big(\frac{\text{dy}}{\text{dx}}\Big)^2\Big\}^{\frac{3}{2}}$

The probability distribution of random variable X is given below:

$\text{X}$	$0$	$1$	$2$	$3$
$\text{P}(\text{X})$	$\text{k}$	$\frac{\text{k}}{2}$	$\frac{\text{k}}{4}$	$\frac{\text{k}}{8}$

Determine the value of k.

Evalute the following integrals:
$\int\sqrt{\frac{1-\cos\text{x}}{1+\cos\text{x}}}\text{dx}$

Find the general solution of the differential equation $y \log y d x-x d y=0$

A particle moves along the curve 6y = x³ + 2. Find the points on the curve at which the y-coordinate is changing 8 times as fast as the x – coordinate.

Write tha value of $\int\sec\text{x}(\sec\text{x}+\tan\text{x})\text{dx}$

Define a reflexive relation.