At stores, Can security ask you to show your handbag if they just suspect you for shoplifting?

Answers:
No, something has to warrant it. They can't just go and search everyone's handbag if they "suspect" it.
More than likely they were monitoring you on CCTV.
Edit; If you say no, there's nothing they can do. They can't detain you, period.

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yes

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Sure. You don't have to show them, but they can ask. Of course, if you refused, they'd probably get suspicious.

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They can ask, but you are well within your rights to say "Piss off, rentacop."
They can arrest you and take you into custody, then search your belongings, but if they're wrong, it's lawsuit time.
If they put their hands on you, you are lawfully allowed to beat them senseless.

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They usually have seen somebody take something and
put it in their shopping bag before they stop them and
ask them to show it. They have to be pretty darn sure
the person has taken or hidden something.

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When you are at a store, your status is generally that of a licensee or an invitee. In those situations, the landowner, i.e., the store, may detain you for a reasonable time and in a reasonable place if there is good cause to suspect you of shoplifting. In so doing, they can certainly ask you to show them your handbag. If you refuse, they don't have much in the way of recourse, but they can hold you in a locked room to question you, for example, without being liable for any sort of lawsuit -- even if you didn't steal anything (as long as their suspicion was reasonable).
That is the general, "common law" rule. If you have questions about a specific incident in a certain jurisdiction, you should call a lawyer