Why is - multiplied by - = +? Plz explain both by algebraic and co-ordinate system.

In the method you gave n^(-1)(-1)=(1/n)^(-1) = n
It should have been (n^-1)^-1 = (1/n)^-1 = n  which leads to prove that reciprocal of reciprocal is number itself

Here is a method to prove algebraically

Basically we need to find
(-1)(-1) = ?

The possible values could be -1 or +1

and the answer is that the following convention has been adopted:

(-1)(-1) = +1

For example, if we adopted the convention that (-1)(-1) = -1, the distributive property of multiplication wouldn't work for negative numbers:

(-1)(1 + -1) = (-1)(1) + (-1)(-1)
	
        (-1)(0) = -1 + -1

              0 = -2

Which is contradiction hence(-1)(-1) = +1