subordinate clauses - I think/know vs. I think/know that

I wonder when verbs like think or know are followed by that; I encountered both forms, is there a difference?

For example,

I know that he did it. // I know he did it.

Are the two sentences both correct?

Answer

Yes, they are both correct. I'd use the second because that's more idiomatic and shorter than the first one. There are times when you don't need "that" in a sentence and this seems to be one of those instances.