Question

The reciprocal of $ - 1$ is $ - 1$ .
(A) True
(B) False

Answer 1

Hint: Whenever there is an integer, we always assume that it is divisible by $1$ . In this question you have to find the reciprocal of $ - 1$ and for that you have to divide $1$ by this number and after dividing you have to see what outcome is coming out be.

Complete step by step solution:
If we want to find the reciprocal of any number, then we have to divide 1 by this number. The reciprocal of any number is the same as the multiplicative-inverse of a number.
Now,
We have to find the reciprocal of $ - 1$.
So, we have to divide it by $1$.
Therefore,
Reciprocal of $ - 1\, = \,\dfrac{1}{{ - 1}}$
Now, multiplying and dividing $\dfrac{1}{{ - 1}}$ by $ - 1$.
Therefore,
$ \Rightarrow \dfrac{{1 \times - 1}}{{ - 1 \times - 1}} = \dfrac{{ - 1}}{1}$
We can also write $\dfrac{{ - 1}}{1}\,\,as\,\, - 1.$
So, we can see that the reciprocal $ - 1$ is $ - 1$.
Therefore, the correct answer is True and the correct option is (A).

Note: Reciprocal is simply defined as the inverse of a value or a number. If n is a real number, then its reciprocal will be $\dfrac{1}{n}$. Thus, here we convert the number into an upside-down form. For example, the reciprocal of \[9\] is $1$ divided by $9$, i.e. $\dfrac{1}{9}$. Now, if we multiply a number by its reciprocal, it gives a value equal to $1$. Thus, it is also called multiplicative inverse. We cannot apply the reciprocal condition on zero, since it will return an indefinite value. Therefore, we can have reciprocal for all real numbers but not for zero.