Elementary Math from an Advanced Standpoint

Guesstimate Question  (no calculator allowed) –

[Hint]: use Abstract Math “Homomorphism”  {f * +}

What is 35823 x 23412 ?

A) 845203402
B) 838688076
C) 812343296

The mapping f defined by
\forall  a_1, a_2, a_3 \in Z
f(a_1a_2a_3) = a_1+ a_2+ a_3
such that,

\forall a, b \in Z,
f (a * b) = f(a) * f(b)

=> f is an homomorphism.

Examples:

f (35823) = 3+5+8+2+3 = 21
f (21)= 2+1= 3

f (23412) = 2+3+4+1+2 =12
f (12) =1+2 = 3

f (35823 x 23412) = 3 x 3 = 9

Verification  (B):
f (838688076)= 8+3+8+6+8+8+0+7+6=54 ..5+4 =9 ☆

Wrong :
f(845203402)= 28…=10 = 1

f (812343296) = 38… =11 =2

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