[{"key":[{a:"a",b:"b"},{a:"c",b:"d"}]},{"key":[{a:"a",b:"b"},{a:"a",b:"b"}]}]

db.collection.aggregate([{$project:{areSame:{$allElementsTrue:{$map:{input:"$key",in:{$eq:["$$this",{$arrayElemAt:["$key",0]}]}}}}}}])