If ab=ab, then ba is called

# If $\frac{a}{b}=\frac{a}{b}$, then $\frac{b}{a}$ is called

1. A

the additive inverse of $\frac{a}{b}$

2. B

the multiplicative inverse of $\frac{a}{b}$

3. C

Both a and b

4. D

multiplicative identity of $\frac{a}{b}$

Register to Get Free Mock Test and Study Material

+91

Live ClassesRecorded ClassesTest SeriesSelf Learning

Verify OTP Code (required)

### Solution:

Since, $\frac{a}{b}=\frac{a}{b}⇒\frac{a}{b}=\frac{a}{b}×1⇒\frac{a}{b}×\frac{b}{a}=1$

$\frac{b}{a}$ is called the multiplication inverse of $\frac{a}{b}$. Hence $\frac{a}{b}×\frac{b}{a}=1$

So $\text{\hspace{0.17em}}\frac{b}{a}$ is not additive inverse of $\frac{a}{b}$ and also

$\frac{a}{b}=\frac{a}{b}⇒\frac{a}{b}+\left(\frac{-a}{b}\right)=0$

So , $\frac{-a}{b}$is additive inverse of $\frac{a}{b}$

But here asked about $\frac{b}{a}$

B: Since $\frac{a}{b}×\frac{b}{a}=1$. Clearly  says that $\frac{b}{a}$is multiplicative inverse of $\frac{a}{b}$

## Related content

 Distance Formula Perimeter of Rectangle Area of Square Area of Isosceles Triangle Pythagoras Theorem Triangle Formulae Volume of Cylinder Perimeter of Triangle Formula Area Formulae Volume Formulae