Product with -1

Task number: 2483

Show that in any field \(\mathbb K\) it holds that \(\forall a\in \mathbb K: (-1)a=-a\).

  • Resolution

    \((-1)a=(-1)a+0=(-1)a+(a-a)=((-1)a+1a)-a=(-1+1)a-a=0a-a=-a\).

Difficulty level: Easy task (using definitions and simple reasoning)
Proving or derivation task
Cs translation
Send comment on task by email