why -1*-1 is equal to +1 ?

Answer 1

We would need some logic on proving this

it's obviously understandable that (+) * (+) = (+) from practical experiences we face always
e.g: when you have 2 piles of 10 books you multiply +2 by +10
to get +20
it's obvious when we deal with objects and when dealing with positive values and + marks we would always get positive values

now the second logic
if (+) * (+) = (+)
what should (+) * (-) be it definitely can't be positive because
positive values com when you multiply (+) * (+)
so it's obvious that it isn't positive, if it isn't positive what can it be? It present human maths there are only 2 types of values which are positive (+) and negative(-) so if (+) * (-) isn't positive it should be negative
so we get (+) * (-) = (-)

now we've understood that (+) * (+) = (+) and
(+) * (-) = (-)

final logic :
if (+) * (-) = (-)
(-) * (-) is not negative it's something else
if it isn't negative what can it be ?
definitely positive
so (-) * (-) = (+)
thus -1 * -1 = +1

Answer 2

Consider -1 divided by -1

-1/-1 = 1 ( the answer is simple nr & deno are same quantity)

-1/1 = -1

Therfore 1/-1 is also -1

if so 1/-1=1
therfore by cross multiplication 1 = -1*-1

A more clear example -10/2 =-5
10/-2=-5

therefore 10 = -2*-5

Note: Negetive numbers were first conceived by Indian Mathematicians. Bhaskara deals with this indetail in his Lilavathy

Answer 3

negative of a number is equivalent to shifting it to the other side of zero in the number line by a distance equal to double the distance between the number and zero.hence sucha shift done twice would give u the same number

Answer 4

A double negative always becomes positive in multiplication and addition. Its the identity property. Both the negative signs cancel out to make it positive.

Answer 5

Because when multiplying, 2 negatives cancel each other and become a positive.

Answer 6

If I give you a rock you have one rock.
If I give you another rock you have two rocks.
If I take away a rock you have one rock.
If I take away a rock you have zero rocks.
If I take away a rock you have ...?
Negative numbers are an abstraction.
They usually signify debt.
If you subtract (take away) that debt it is essentially the same thing as giving (adding to) you that thing in an absolute sense.

Answer 7

I just answered this question in the math section about a minute ago, so check out my last answer.

Answer 8

Because " A (Negative) (Negative) = (Positive)