different between (-(a.b)) and ((-a).b)

Question

One of our teachers said that there is just one example that there is different between $(-(a\cdot b))$ and $((-a)\cdot b)$. He said by using "twice complement," you can find one.

I am trying to find this example. Can anyone please help me?

Thanks in advance

Answer 1

I noted one difference between the two in the realm of abstract algebra.

$-(a\cdot b)$ is the additive inverse of$a\cdot b$

While the other is the product of the additive inverse of $a$ to $b$.

That's there difference in context.But nontheless they are equal by a theorem in abstract algebra.