You can always try as follows:
SELECT TT.produto
, TT.matricula
, TT.data
, TT.fornecedor
, TT.contador
FROM tb_teste TT
INNER JOIN (
SELECT COUNT(1) AS contador
, produto
, matricula
FROM tb_teste
GROUP BY produto
, matricula
) TT2 ON TT2.produto = TT.produto
AND TT2.matricula = TT.matricula
WHERE TT2.contador > 1
ORDER BY TT.fornecedor
But then you will only have the link for the product and registration, I do not know if it will be enough.
The way I wanted to do it initially is impossible. If you want to count the records based on certain fields, they all have to be in GROUP BY
otherwise you will not be able to execute the query .