If L={a+b+} then LR={b+a+}
So L contains strings {ab,aab,aaab,abbb...} and LR={ba,baa,bba,...}
No strings common.
If L={a+} then LR={a+}
So L contains strings {a,aa,aaa...} and LR contains {a,aa,aaa...}
All strings common.
So S1 is false.
If L1={a} and L2={a*}
Then L1L2={aa*} and L2L1={a*a} Both are same hence commutative in this case also..
S2 is false..