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Would anyone please tell me if "to mistake something" and "to be mistaken about something" mean the same or if there's any difference between them?

For example, I'm providing you with sentences:

1a. I mistook her signature on the envelope and thought it was somebody else's.

1b. I was mistaken about her signature and thought... .


2a. You can't mistake their house - it has a big yellow gate.

2b. You can't be mistaken about their house - it has a big yellow gate.


3a. If I am not mistaking it, she is one of the top rankers of the University.

3b. If I am not mistaken about it, she is one of the top rankers of the University.



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LaboriousWould anyone please tell me if "to mistake something" and "to be mistaken about something" mean the same or if there's any difference between them?

They strike me as a bit different.

You mistake something for something else.
You are mistaken about something.

LaboriousI mistook her signature on the envelope and thought it was somebody else's.
I was mistaken about her signature and thought...

I'd just say I mistook her signature ... for someone else's.

In my opinion, the second version doesn't work as well, but it's not wrong.

I would use the second version when commenting on a single thing or category of thing.

Sorry I'm late. I was mistaken about the time.
I can't believe I said it was blue. Now that I see it again in the light, I can see that I was obviously mistaken about the color.

LaboriousYou can't mistake their house - it has a big yellow gate.

OK. for anybody else's is implicit.

You can't be mistaken about their house seems like an unnecessary use of words, but it's not wrong.

LaboriousIf I am not mistaking it, ...
If I am not mistaken about it, ...

The usual "canned phrase" is simply If I'm not mistaken, .... I'd just leave it at that. ("If it ain't broke, don't fix it!")

CJ

Laboriousshe is one of the top rankers of ...

It's unrelated to your question, but this phrasing doesn't sound right to my ear.

I am used to hearing this:

she is in the top ranks of ...

CJ

Comments  
Laborious1a. I mistook her signature on the envelope and thought it was somebody else's.

I can't call that wrong, exactly, but it sounds like a roundabout way of putting the simpler "I mistook her signature on the envelope for somebody else's."

Laborious1b. I was mistaken about her signature and thought... .

If you mean the same as number 1, no. If you thought it was someone else's, this sounds like you don't know the plain way of putting it. If you were in error about her signature in some other aspect, it's fine.

Laborious2a. You can't mistake their house - it has a big yellow gate.

Good. This means that you will have no trouble telling which house is theirs.

Laborious2b. You can't be mistaken about their house - it has a big yellow gate.

No, if you mean the same as 1. But if you had previously said, for instance, that their house had a big green gate, then it's fine.

Laborious3a. If I am not mistaking it, she is one of the top rankers of the University.

Unidiomatic.

Laborious3b. If I am not mistaken about it, she is one of the top rankers of the University.

Almost. The usual way of putting that is "If I am not mistaken, she is one of the top rankers of the University." Adding "about it" sounds unnatural.

 CalifJim's reply was promoted to an answer.