Q. Prove : (- 1) $\times$ (- 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) $\times$ (- 1) = 1

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)