Let 'o ' be a binary operation on the set Q_0 of all non-zero rat… - Vidyadip

Question

Let $'o\ '$ be a binary operation on the set $Q_0$ of all non$-$zero rational numbers defined by $\text{a}\ ^*\ \text{b}=\frac{\text{ab}}{2} $ for all $\text{a},\text{b}\in\text{Q}_0.$
Find the identity element in $Q_0.$

✓

Answer

We have,
$\text{a }^*\text{ b}=\frac{\text{ab}}{2}$ for all $\text{a},\text{b}\in\text{Q}_0$
Let $\text{e}\in\text{Q}_0$ be the identity element with respect to $*.$
By identity property, we have,
$a * e = e * a = a$ for all $\text{a}\in\text{Q}_0$
$\Rightarrow\frac{\text{ae}}{2}=\text{a}\Rightarrow\text{e}=2$
Thus the required identity element is $2.$

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 Questions" from Binary Operations→Binary Operations — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Find $\frac{d y}{d x}$ if $\sin^2 y + \cos xy = \kappa$

Evalute the following integrals:
$\int\sqrt{\frac{1+\cos2\text{x}}{1-\cos2\text{x}}}\text{dx}$

One card is drawn at random from a well shuffled deck of 52 cards. In which of the following cases are the events E and F independent?
E: ‘the card drawn is a spade’
F: ‘the card drawn is an ace’

If $|\vec{\text{a}}|=10,\big|\vec{\text{b}}\big|=2$ and $\big|\vec{\text{a}}\times\vec{\text{b}}\big|=16,$ find $\vec{\text{a}}.\vec{\text{b}}.$

If $\vec{\text{a}}\text{ and }\vec{\text{b}}$ represent two adjacent sides of a parallelogram, then write vectors representing its diagonals.

If a line makes angles $90^\circ$ and $60^\circ$ respectively with the positive direction of $x$ and $y$ axes, find the angle which it makes with the positive direction of $z-$ axis.

If A' = $\left[\begin{array}{cc} {-2} & {3} \\ {1} & {2} \end{array}\right] \text { and } \mathbf{B}=\left[\begin{array}{rr} {-1} & {0} \\ {1} & {2} \end{array}\right]$, then find (A + 2B)′

For the principal values, evaluate the following:
$\cos^{-1}\frac{1}{2}+2\sin^{-1}\Big(\frac{1}{2}\Big)$

Let $\text{f(x)=}\begin{cases}1+\text{x,}&0\leq\text{x}\leq2\\3-\text{x,}&2<\text{x}\leq3\end{cases}.$ Find fof.

If $A$ is a non$-$singular square matrix such that $\text{A}^{-1}=\begin{bmatrix} 5 & 3 \\ -2 & -1 \end{bmatrix},$ then find $(A^T)^{-1}.$