Kate Hudson and Matt Bellamy -- Off the Market and In the Market

Kate Hudson and Matt Bellamy gave everyone a big fat clue about their relationship status ... by doing something a freshly broken up couple doesn't do ... grocery shopping.

It sure looked like they had broken up last month ... Matt seemed downright giddy about being single. But things took a dramatic turn Sunday at a Brentwood supermarket, when the 2 shopped together, loaded their groceries in the same car and drove off.

It could be a co-parenting thing -- they have a 3-year-old son together -- but a shopping trip sure seems super domestic.

There were reports Hudson was hanging with "Dancing with the Stars" star Derek Hough ... but lately it seems it's all about Kate and Matt. They were in Aspen together over the holidays with their son.

Either the holidays have rekindled that flame ... or they found a REALLY good deal on macaroni and cheese.