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**Hint:**We have to find the multiplicative inverse of $ - 1 \times \dfrac{{ - 2}}{5}$. Multiplicative inverse of a number is obtained when \[1\] is divided by the given number that is, the multiplicative inverse of a number $x$ is $\dfrac{1}{x}$. After getting the value of the inverse of the given number, we have to equate the result with the $\dfrac{p}{2}$. Then solving the equation we will get the required value of $p$.

**Complete step-by-step solution:**

It is given that the multiplicative inverse of $ - 1 \times \dfrac{{ - 2}}{5}$ is $\dfrac{p}{2}$. And we have to find the value of $p$.

First of all, find the multiplicative inverse of the given number $ - 1 \times \dfrac{{ - 2}}{5}$.

As multiplication of two negative numbers gives the positive number so, $ - 1 \times \dfrac{{ - 2}}{5}$ can be written as $\dfrac{2}{5}$.

Now, to get the multiplicative inverse of $\dfrac{2}{5}$, divide $1$ by $\dfrac{2}{5}$. That is

$

= 1 \div \dfrac{2}{5} \\

= 1 \times \dfrac{5}{2} \\

= \dfrac{5}{2}

$

So, we get the multiplicative inverse of $ - 1 \times \dfrac{{ - 2}}{5}$ is $\dfrac{5}{2}$.

Now, to find the value of $p$equate the obtained multiplicative inverse to the $\dfrac{p}{2}$ because it is given that $\dfrac{p}{2}$ is the multiplicative inverse of given number$ - 1 \times \dfrac{{ - 2}}{5}$.

$

\Rightarrow \dfrac{5}{2} = \dfrac{p}{2} \\

$

Solving this by cross multiplication, we get

$

\Rightarrow p \times 2 = 5 \times 2 \\

\Rightarrow p = \dfrac{{5 \times 2}}{2} \\

\therefore p = 5

$

**Thus, the required value of $p$ is $5$.**

**Note:**The multiplicative inverse of the number is a particular number which when multiplied with the given number we get one as a result. That is, if the multiplicative inverse of the number $x$ is a number $y$ then $xy = 1$.

Similarly, we can find the additive inverse of a number which is obtained by subtracting the given number from zero.

Additive inverse of a number is a particular number which when added with the given number we get zero as a resultant. That is, if the additive inverse of a number $x$is a number $y$then $x + y = 0$.

Simply, we can say the additive inverse of $x$ is $ - x$.

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