Is a color singlet state invariant under a unitary matrix?

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james228
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TL;DR
After applying U on the color singlet state I am not getting the same color singlet state back. How can i show this color singlet state is actually invariant under U?
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You should show us your work, then we may be able to see what's going on.
 
I did figure it out. Thank you so much!
 

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