SATS again

This is a sort of follow-up to my post dated 27/1/12, which you might like to read first. Embarrassment for the Schools Minister when he apparently failed to correctly answer the following question from the Key Stage 2 (7 to 11-year-olds) grammar test - "I went to the cinema after I'd eaten my dinner."  Is the word "after" here being used as a subordinating conjunction or as a preposition?  Can I suggest a third possible answer - Does it in any way matter if I don't know?