Promo: Why does a negative times a negative equal a positive? Video Lecture | Sets and Functions - JEE

why does a negative times a negative
equal a positive this rule is not just
made up there is a chain of reasoning a
mathematical argument that shows why the
rule has to be that negative times
negative equals positive here's how the
reasoning goes zero times anything
equals zero every number has exactly one
additive inverse this means that if M is
a positive number then minus M is its
additive inverse so that M plus minus M
equals zero likewise the additive
inverse of minus M is M we want negative
numbers to obey the distributive law
this says that the product of a and B
plus C equals a times B plus a times C
consider the expression the product of 2
+ 1 + -1 this equals 2 times 0 which is
0 but by the distributive law it equals
2 times 1 plus 2 times minus 1 so 2
times minus 1 does the job of additive
inverse of 2 times 1 and therefore 2
times minus 1 is the additive inverse of
2 times 1/2 times 1 equals 2 and the
additive inverse of 2 is minus 2 since a
number has exactly one additive inverse
2 times minus 1 equals -2 therefore we
have to accept that negative times
positive equals negative
now consider the expression the product
of -2 + 1 + minus 1 this equals minus 2
times 0 which is 0 using distributive
law we can write this expression as
minus 2 times 1 plus minus 2 times minus
1 so minus 2 times minus 1 does the job
of additive inverse of minus 2 times 1
and therefore minus 2 times minus 1 is
the additive inverse of minus 2 times 1
from the previous reasoning we know that
minus 2 times 1 equals minus 2 and minus
2 has exactly 1 additive inverse which
is 2 so minus 2 times minus 1 equals 2
so we have to accept the law that
negative times negative equals positive