why minus multiply minus is plus ?

First see this pattern 

                                         
                                          Decreasing Pattern of positive number

5 × 4 = 20

5 × 3 = 15

5 × 2 = 10

5 × 1 = 5

5 × 0 = 0

So, using the pattern,

5 × − 1 = − 5

5 × −2 = −10

 5 × −3 = −15

 5 × −4 = −20

Increasing Pattern of negative number.

−5 × 4 = −20

 −5 × 3 = −15

−5 × 2 = −10

−5 × 1 = −5

−5 × 0 = 0

so, using the pattern,

−5 × −1 = 5

−5 × −2 = 10

 −5 × −3 = 15

 −5 × −4 = 2

We see this type of pattern we conclude that 

(+) × (+)=(+).

 (−) × (−)=(+). 

(+) ÷ (+)=(+).

 (−) ÷ (−)=(+). 

 and

(+) × (−) =(−)

(−) × (+)=(−)

 (+) ÷ (−)=(−)

 (−) ÷ (+)=(−)  

Alternative method of (-) ×(-)=(+)

In extending form positive whole number to integer we prescribe all the rule of arithmetic expect come one.

The rule we give is 

                      No number comes before 0.

But we have 

1. a×0=0×a=0 for all a. So particular 1×0=0
2. 1×a=a×1=a for all a . so Particular -1×1=1×-1=-1
3. Also Distributive Law a×(b+c)=(a×b)+ (a×c)

Consider,

-1×(-1+1)

This is -1×0=0 [by 1]

By Distribute law 

-1×(-1+1)=(-1×-1)+(-1×1) then last term is -1 [by 2]

i.e. 0=(-1×-1)+(-1)

Hence, -1×-1=1