Pandigital products

We shall say that an \( n \)-digit number is pandigital if it makes use of all the digits \( 1 \) to \( n \) exactly once; for example, the \( 5 \)-digit number, \( 15234 \), is \( 1 \) through \( 5 \) pandigital.

The product \( 7254 \) is unusual, as the identity, \( 39×186=7254 \), containing multiplicand, multiplier, and product is \( 1 \) through \( 9 \) pandigital.

Find the sum of all products whose multiplicand/multiplier/product identity can be written as a \( 1 \) through \( 9 \) pandigital.

HINT: Some products can be obtained in more than one way so be sure to only include it once in your sum.