Cryptarithmetic rules

Rule-1
If  A + B = A  then the possible value of B={0, 9}
Case I 
i.e. K + A = A (K=0)
Example Supporting Case-I 
                      P  A  S
                   x  R  B  Q
                   S  B  K  W
                A  S  A  A 
             S  E  P  B      
             S  Q  S  K  A  W
Here, you can easily predict the value of K = 0

Case II 

If A + B = A
When B = 9  9 + A = A   [9 + A + 1(carry) = _A]
When you have 1 carry from the previous addition.
Example supporting Case-II
                                                3  5 
                                               +9  7
                                             1  3  2
Example:

                      A  I  D
                      x  A  D
                   R  I  A  D
                D  D  C  D      
                D  I  C  E  D

Here, you can take I=9 as I + C = C

Rule-2
If A * A = _A  then the possible value of A={1, 5, 6}
Case I 
      1.    When A=1   1 * 1 = _1  

Case II
      1.    When A=5   5 * 5 = _5 (25) [consider last digit only]
      2.    When A=6   6 * 6 = _6 (36) [consider last digit only]

Example supporting Case-II
 
                       T  E  A
                    x  H  A  D
                    L  D  T  R
                 H  R  S  A
              E  W  D  A        
              L  E  S  S  E  R


In this problem, you can easily predict value of A={5, 6}