I am graduate student.

As you know, the convolution operation satisfy the below equation due to commutative raw.
a(n)*b(n)*c(n) = a(n)*c(n)*b(n) 

In addition, the muliplication operation also satisfy the below equation due to commutative raw.
a(n)b(n)c(n) = a(n)c(n)b(n) 

however, to my knowledge, the below equation was not satisfied; 
a(n)b(n)*c(n) = a(n)*c(n)b(n) 

Can I say that "the commutative raw between multiplication operation and convolution operation does not satisfied" ?

Futhermore, do you know any reference for this phenomenon?

Best Regards,