Question

$1$ is the only number which is its own reciprocal. State whether the statement is true (T) or false (F).

• A. True
• B. False

Answer 1

The correct option is B False

Verify the given statement

Let us assume that $x$ is a real number.

Thus, the reciprocal of the number will be $\frac{1}{x}$.

If the given number and its reciprocal are the same, then $x=\frac{1}{x}$.

$$\begin{gathered} \Rightarrow x·x=1 \\ \Rightarrow x^2=1 \\ \Rightarrow x=\pm \sqrt{1} \\ \Rightarrow x=\pm 1 \end{gathered}$$

Therefore, $1$ is not the only number that is its own reciprocal.

Hence, the given statement is false.