A Deduction Problem

AZA
x AZZA
AZZZZZA

Substitute a single digit for Z.  Substitute any digit for each A.  The number for Z must be different from the numbers for A.  There are no leading zeros.  What are the possible solutions?

Source: Reader Jimmy Chng Gim Hong, though I believe I've seen it elsewhere.

Solutions were received from Claudio Baiocchi, Toby Gottfried, Denis Borris, Philippe Fondanaiche, Adrian Atanasiu, Alan O'Donnell, Sandy Thompson, Paul Botham.

There are only two solutions:

723 * 7223 = 5222229
645 * 8441 = 5444445

Mail to Ken