Products of 2-Digit Pairs which Reversed reveal Same Product

Theorem
The following positive integers can be expressed as the product of $2$ two-digit numbers in $2$ ways such that the factors in one of those pairs is the reversal of each of the factors in the other:
 * $504, 756, 806, 1008, 1148, 1209, 1472, 1512, 2016, 2208, 2418, 2924, 3024$

Proof
Let $n \in \Z_{>0}$ such that:
 * $n = \left[{a b}\right] \times \left[{c d}\right] = \left[{b a}\right] \times \left[{d c}\right]$

where $\left[{a b}\right]$ denotes the two-digit positive integer:
 * $10 a + b$ for $0 \le a, b \le 9$

from the Basis Representation Theorem.

We have:

Thus the problem boils down to finding all the sets of one-digit integers $\left\{ {a, b, c, d}\right\}$ such that $a c = b d$, and so that:


 * $n = \left[{a b}\right] \times \left[{c d}\right] = \left[{b a}\right] \times \left[{d c}\right]$

and also:
 * $n = \left[{a d}\right] \times \left[{b c}\right] = \left[{d a}\right] \times \left[{c b}\right]$

Thus we investigate all integers whose $\tau$ value is $3$ or more, and find all those which have the product of single-digit integers in $2$ ways, as follows:

Further integers $n$ such that $\tau \left({n}\right) \le 4$ need not be investigated, as one of the pairs of factors will be greater than $9$.