" "I have done this" is not an expression to my knowledge.
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Anonymous is it possible to say : I can have done thisIt is possible that your native language leads you to use can in your last example. A word-for-word translation from some languages may prompt you to use can in the sentence. I wonder if you mean to say: I may have done this.
Anonymousis it possible to say : I can have done thisNo. For some strange reason, we don't use "can have X", where X is a past participle. Substitute one the following:
Anonymouswe can say : I cant' have done this
but is it possible to say : I can have done this
AnonymousI disagree. The sentence I can't have done this is correct and expresses a negative deduction about an event in the past: ' Where can I have put the remote control?' 'I can't have thrown it away.'Anon,