a.0 = 0

a.0 = 0
1. 1+0=1       //assume
2. a(1+0)=a.1  //1 multiply by a
3. a.1+a.0=a.1  //2 distributive law
4. a+a.0=a      //3 multiplicative identity
5. a+(-a)+a.0=a+(-a)  // add -a to 4
6. 0+a.0=0    //by 5 additive inverse
7. a.0=0    //by 6 additive identity

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