Find the multiplicative inverse (or reciprocal) of:

$\dfrac{-3}{-5}$

To find the multiplicative inverse (or reciprocal) of a non-zero rational number, interchange its numerator and denominator.

First express the rational number with a positive denominator.

$\dfrac{-3}{-5} = \dfrac{-3 \times (-1)}{-5 \times (-1)} = \dfrac{3}{5}$

Interchanging the numerator and the denominator of $\dfrac{3}{5}$, we get $\dfrac{5}{3}$.

$[\text{Check : } \dfrac{3}{5} \times \dfrac{5}{3} = 1]$

Hence, the multiplicative inverse of $\mathbf{\dfrac{-3}{-5} \text{ is } \dfrac{5}{3}}$.