He must have been at home all day last night的反义疑问句怎样问?

He must have been at home all day last night的反义疑问句怎样问?

He must haven't been at home all day last night.

呃……我觉得是mustn't he 。。。。
must不是情态动词吗？有情态动词应该是用情态动词吧，didn't 和wasn't都不对啊。。。。。。。。。

Shouldn't he have been at home all day last night?