Q. Prove : (- 1) $×$ (- 1) = 1. Please experts, answer this, according to the context or reference given in the picture. Euler in his Ankitung zur Algebra(1770), was one of the first mathematicians to attempt to prove (- 1) $×$ (- 1) = 1

Hi,

From the distributive law of multiplication we have

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

which holds for all real numbers. So it will hold if we put a=-1, b=1 and c=-1

(-1)*(1+(-1)) = (-1)*1 + (-1)*(-1)

1+(-1) = 0 and -1*1 = -1 so we get

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

rearrange to get

1 = (-1)*(-1)

• 1
-1x-1=
Minus symbol is cancelled both sides
1x1=1

• -1
Thank to answer. But, it just a rule to remember. But I want it's proof as given in the Ankitung Zur Algebra.
• 0

(-1)*(-1) = 1*1
= 1
= (negative into negative= positive)
= SO,  the answer is +1

• 0
-1*-1=1
because
when 1*1=1
then -1*1=-1
but in -1*-1=1
then the minus symbol is cancelled because there are two minus sign

• 0
I know that (-)*(-) = (+)... But I want the proof of this law from the mentioned book ..
• 0
It is a rule that if there is 2 minus or negative sign in a algebric multipilcation the answer will be always in positve just like (-2) ? (-3) = 6. This is an algebric rule.
• 0
What are you looking for?