Question

prove that (a+b)-¹(a-¹+b-¹)=(ab)-¹​

Answer 1

Answer:

Step-by-step explanation:

I want to show (ab)−1 = b−1a−1.

I originally thought of proving the fact in the following manner:

(ab)−1(ab)(ab)−1(ab)(b−1)(ab)−1(a)(bb−1)(ab)−1(a)(e)(ab)−1(a)(ab)−1(a)(a−1)(ab)−1(e)(ab)−1=e=(e)(b−1)=(b−1)=(b−1)=(b−1)=(b−1)(a−1)=(b−1)(a−1)=(b−1)(a−1)

I know this may seem extremely inefficient to most, and I know there is a shorter way. But would this be considered a legitimate proof?

Thanks in advance!