Assertion (A) : (p - q)^-1 (p^-1 - q^-1) = -(pq)^-1.

Reason (R) : a^-1 and a¹ are multiplication reciprocal to each other.

1. Both A and R are correct, and R is the correct explanation for A.

2. Both A and R are correct, and R is not the correct explanation for A.

3. A is true, but R is false.

4. A is false, but R is true.

According to assertion : (p - q)^-1(p^-1 - q^-1) = -(pq)^-1

Solving L.H.S.,

$\Rightarrow (p - q)^{-1}(p^{-1} - q^{-1})\\[1em] \Rightarrow \Big(\dfrac{1}{p - q}\Big)\Big(\dfrac{1}{p} - \dfrac{1}{q}\Big)\\[1em] \Rightarrow \Big(\dfrac{1}{p - q}\Big)\Big(\dfrac{q - p}{pq}\Big)\\[1em] \Rightarrow -\Big(\dfrac{1}{p - q}\Big)\Big(\dfrac{p - q}{pq} \Big)\\[1em] \Rightarrow -\dfrac{(p - q)}{pq(p - q)}\\[1em] \Rightarrow -\dfrac{1}{pq}\\[1em] \Rightarrow -(pq)^{-1}$

Since, L.H.S. = R.H.S.

So, assertion (A) is true.

Multiplying a^-1 and a¹, we get :

⇒ a^-1 x a¹

⇒ $\dfrac{1}{a}$ x a

⇒ 1

Thus, a^-1 and a¹ are multiplication reciprocal to each other.

So, reason is true but it does not explains assertion.

Hence, option 2 is the correct option.