Is $r(^∗)=r^∗$ valid regular expression?

Question

Which of the following regular expression identities is/are TRUE?

1. $r(^∗)=r^∗$
2. $(r^∗s^∗)=(r+s)^∗$
3. $(r+s)^∗=r^∗+s^∗$
4. $ r^∗s^∗=r^∗+s^∗$

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My attempt :

1. I can't say anything, but it should be invalid.
2. $LHS\subset RHS$
3. $RHS\subset LHS$
4. $RHS\subset LHS$

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My question is :

Can you explain in formal way, please?

As definition given on wiki : Regular expressions consist of constants and operator symbols that denote sets of strings and operations over these sets, respectively.