Prove (-1) * (-1) = 1

CoolMyth SG

Ever thought why this is true? Now try your hand at proving it.

Some hints:

Let a, b and c be numbers and -a, -b and -c be its negative respectively.

i) a + (-a) = 0 (Obvious, right? Laughing )

ii) a*(b+c) = a*b + a*c

iii) a + c = b + c a = b

Okay, now try proving (-1) * (-1) = 1 using the above hints. But in your proof, don't ever use (-1) * (-1) = 1.

hisoka SG

erm ok use 1 and 2

b=a and c = -a

so a^2 +a(-a) = 0

a^2= (-1).(-1).a^2

therefore (-1).(-1) = 1??

CoolMyth SG

By shifting the part in red to the other side, you're indirectly implying that

1 = -(-1) = (-1) * (-1), which is the question itself.

So, it's not correct, sorry, but it's a good effort. Mr. Green

Note, a, b and c are just numbers, you're supposed to substitute appropriate values for them and use the hints given.

hisoka SG

huh?? dun get what you mean

what i did was to add both sides with the term i wanna appear on the right so no implied of the 1 =-(-1)

CoolMyth SG

EDIT: Finally saw something wrong.

Okay. Here's how it goes:

You were actually using the fact that (-1)a = -a, which is not of my hints given.

Sorry.

hisoka SG

wrong marking request to strip you of job Laughing

CoolMyth SG

Proof of (-1)*a = -a. (Different from question)

From a + (-a) = 0

--> [a + (-1)*a] + (-a) = (-1)*a (Add (-1)*a on both sides)

--> [a(1 + (-1)] + (-a) = (-1)*a

--> a*0 + (-a) = (-1)*a

--> 0 + (-a) = (-1)*a

--> (-1)*a = -a

ndmmxiaomayi SG

I'm stumped. Embarassed

hisoka SG

you never say cannot use other such terms wor Rolling Eyes

CoolMyth SG

I got say use the above hints mah.

Then you used another one.... Laughing

Okay lah, correct lah, correct lah. Happy?