2011/039) prove that (-1)* (-1) = 1

a lot of proof of the same is there including the proof below

we know
(-1) + 1 = 0

multiply both sides by -1 to get
(-1)*(-1) + 1*(-1) = 0
add 1* (1) on both sides

to get (-1)*(-1) + 1*(-1) + 1* (1) = 1
or (-1)*(-1) + (1*(-1) + 1* (1))= 1
or(-1)*(-1) + 0= 1

or (-1)*(-1) = 1

proved

However all the proofs including the above come from back ward calculation from LDMA
The LDMA shall fail unless we define it the above way which is a big sacrifice and hence it need to be defined this way to maintain the consistency of LDMA.

( similarly 0! is defined to be 1 so that law of combinatorial holds