Check for accuracy of a product

Subject:  How to check for the accuracy of product of two numbers.
                   Example           123476
                                              x 654879
                                            7645983254
      Now to check for the accuracy no need to go to the actual product. Follow the following simple steps.
1.    add all the digits of the first number i.e. 1+2+3+4+7+6= 23
2.  divide it by 9 and record the remainder i.e. 23 /9 , remainder = 5
3. add all the digits of second number 6+5+4+8+7+9 = 39
4.  divide it by 9 and record the remainder i.e. 39 /9 , remainder = 3
5.  multiply the two remainders i.e. 5x3 = 15
6.  divide the number obtained in step 5 by 9 and record the remainder. i.e. 15/9, remainder = 6
7.  add all the digits of the product of two numbers i.e. 7645983254 you get
      7+6+4+5+9+8+3+2+5+4= 53
8.  divide it by 9 and record the remainder i.e. 53 /9 , remainder = 8
Conclusion: If remainders obtained in step 6 and 8 are equal then your product is correct otherwise wrong.
Clearly above product is wrong. As remainder in step 6 is and that in step 8 is 8 , unequal.