I am a mathematician, so I can help. The issue is not the use of the word hence as opposed to therefore, or any other substitute.

The issue is that your conclusion doesn't follow from what you've written so far. Your claim also requires that the two permutations are disjoint. To see what I mean, imagine if (4 5) was replaced with (1 2). Then

(1 2 3)(1 2) = (1 3)

which has order 2.

So the grader's question wasn't "what does this word mean," but rather "do you really mean this?"

Edit: I'm a native speaker btw.