Show that (-1)(-1) = 1

[lookagain]

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Show that (-1)(-1) = 1


Start with what you know:
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1 multiplied by any integer equals that integer.

0 multiplied by any integer equals 0.

For any integer a, \(\displaystyle \ \ \)a + (- a) = 0

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Start with a true statement:


\(\displaystyle \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \)\(\displaystyle 0 = 0\)

\(\displaystyle \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \)\(\displaystyle 1 \ + \ (- 1) = 0\)

\(\displaystyle \ \ \ \ \ \ \)\(\displaystyle [1 \ + \ (- 1)](-1) = 0(-1)\)

\(\displaystyle 1(-1) \ + \ (-1)(-1) = 0\)

\(\displaystyle \ \ \ \ \ \)\(\displaystyle -1 \ + \ (-1)(-1) = 0\)

\(\displaystyle \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \)\(\displaystyle (-1)(-1) = 1\)

 

[daon2]

How do you know equality is reflexive without it being an assumption? How do you go from line 2 to 3 if you don't know that a=b implies ac=bc? How do you go from line 3 to 4 without knowing the distributive property? How do you go from line 5 to 6 without knowing a=b implies a+c=b+c??

 

[greg1313]

How do you know ...? How do you ...? How do you ...? How do you ...?

The OP knows it well already and doesn't need to bring it up.