MathsGee is Zero-Rated (You do not need data to access) on: Telkom |Dimension Data | Rain | MWEB

0 like 0 dislike
48 views
Why is $-1 \times -1 = 1$?
| 48 views

1 like 0 dislike

There are a few basic assumptions we need to make:

1. $-x$ is the number that satisfies $(-x) + x = 0$ for any $x$.
2. $1$ and $0$ satisfy: $1 \cdot x = x$ and $0 \cdot x = 0$ for any $x$.
3. Multiplication and addition satisfy the distributive law, i.e. $(a + b) \cdot c = ac + bc$ for any $a, b, c$.

Then, for any $x, y$,

$$(-x) \cdot y + x \cdot y = (-x + x) \cdot y = 0 \cdot y = 0.$$

So $(-x) \cdot y = - (x \cdot y)$ for any $x, y$.

In particular, $(-1)\times (-1) = - (1 \times (-1)) = -(-1) = 1$

by (112 points)

0 like 0 dislike