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Is it legal for declarer to look at his/her last card played after the cards from that round are all face down?

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Yes, as noted in Law 66 B of The Rules of Duplicate Bridge, with a certain restriction:

B. Own Last Card

Until a card is led to the next trick, declarer or either defender may inspect, but not expose, his own last card played.

As the collection of tricks is mechanically different under the Laws of Rubber Bridge Law 66 - Inspection of Tricks is similarly a bit different:

Law 66 – Inspection of Tricks

Declarer or either defender may, until a member of his side has led or played to the following trick, inspect a trick and inquire what card each player has played to it. Thereafter, until play ceases, quitted tricks may be inspected only to account for a missing or surplus card. ....

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