Is there a formal proof for ( 1)×( 1)=1 If yes, then answer Please don't copy from internet - Maths - Integers

Question

Is there a formal proof for (−1)×(−1)=1 If yes,
then answer Please don't copy from internet or Don't tell that
(-)*(-)=+ as I have asked to tell the formal proof

Brijendra Pal · Accepted Answer

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)

Is there a formal proof for (−1)×(−1)=1. If yes, then answer. Please don't copy from internet or Don't tell that (-)*(-)=+ as I have asked to tell the formal proof.