Question

The product of non zero rational number and its multiplicative inverse is always

Answer 1

1 is the answer

if X is a nonzero rational number and 1/X is its multiplicative inverse a

then (x)(1/X)=1

Answer 2

The product of non zero rational number and its multiplicative inverse is always 1 (one)

Given :

A non zero rational number

To find :

The product of non zero rational number and its multiplicative inverse

Solution :

Step 1 of 2 :

Define multiplicative inverse of a non zero rational number

1 is the Multiplicative identity

Let N be a non zero rational number

Also let M is the multiplicative inverse of N ( ≠ 0 )

Then M × N = 1 = N × M

⇒ M = 1/N

So 1/N is multiplicative inverse of N

Step 2 of 2 :

Find the product of non zero rational number and its multiplicative inverse

We see that , for a non zero rational number N the multiplicative inverse of N is 1/N

Therefore the product of non zero rational number and its multiplicative inverse

$\displaystyle \sf{ =N \times \frac{1}{N} }$

$= 1$

Hence the product of non zero rational number and its multiplicative inverse is always 1

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